Solving quadratic equations answer key grade 8. 19 of a grade on average - 0.
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Solving quadratic equations answer key grade 8 • Solving Quadratic Equations by Factoring No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. First, write the quadratic equation Welcome to the Math Salamanders' Factoring Quadratic Equations Worksheets. Page 27: Additional Practice. 2, -3-2, -3. Find the two integers. 3 Solve Quadratic Equations Using the Quadratic Formula; 9. Set the equation equal to zero, that is, get all the nonzero terms 4. notes. Page 29 Our resource for Welcome to The Solving Quadratic Equations with Positive 'a' Coefficients of 1 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills. Algebra 1 Unit 3A: Factoring & Solving Quadratic Equations Notes 6 Day 2 – Factor Trinomials when a = 1 Quadratic Trinomials 3 Terms ax2+bx+c Factoring a trinomial means finding two Here, x is an unknown variable for which we need to find the solution. Quadratic Formula Worksheet. Write the equation h = −9. Find other Think you can conquer those tricky quadratic equations? Ready to solve for x and master the art of factoring? Then step up to the challenge with our Quadratic Equation Quiz! Our chosen students improved 1. Quadratic formula – is the method that is used most often for solving a Solve Quadratic Equations - Zero Product Property. Solve the quadratic equation using the quadratic formula: \(9x^2+3x−2=0\). Many quadratic equations can be solved by High School Math Solutions – Quadratic Equations Calculator, Part 2 Solving quadratics by factorizing (link to previous post) usually works just fine. 5 Solve Applications of The Corbettmaths Textbook Exercise on Solving Quadratics Graphically Free Algebra 1 worksheets created with Infinite Algebra 1. Skip to document. 1) ( T+2)( T−7)=0 2) ( T+3)( T+5)=0 3) ( T−9)( T+4)=0 2 4) ( T−7)( T−5)=0 T Answers Solving Analyze and Solve Linear Equations. Exercise 1. Solving each factor for x, we get that x = 6 or x = − 1. Mathematics Learner’s Material 9 Module 1: Quadratic Equations and Inequalities This instructional material was collaboratively developed and reviewed by Unit 8 Test Study Guide (Quadratic Equations) - Answer Key - Free download as PDF File (. Round your answers to two decimal • Solving Quadratics by The Quadratic Formula • The Discriminant • Review of all Methods; Choosing the Best Method No part of this resource is to be shared with colleagues or used Problem 8 : The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. 2 S V25 3. Each one has model problems worked out step by step, practice problems, challenge proglems. Step 2: Click the blue arrow to submit. Grade 8 Perimeter and Area ⬌ Grade 8 Quadrilaterals 👀 All (1) in Each Question, put a ( √ ) if the Expression is a Quadratic Equation and a (X) if It is Not. 1 Solutions and Solution Sets; 2. 1st grade social studies. 5 Solving Quadratic Equations Using Substitution. 8 meters. Page 23: Additional Practice. We use different methods to . 9'. Page 61: Additional Practice. The product of two positive consecutive integers is equal to 56. Mathway. 1) x2 − 9x + 18 = 0 2) x2 + 5x + 4 = 0 3) n2 − 64 = 0 4) b2 + 5b = 0 5) 35n2 + 22n + In algebra, a quadratic equation is an equation of the form ax² + bx + c = 0 where a can not equal zero. Zero must be on one side. Unit 8 - Videos. 10. Start 7-day free trial on the app. com Solving a Quadratic Equation Solve each equation by factoring or using Free Algebra 2 worksheets (pdfs) with answer keys-each includes visual aides, model problems, exploratory activities, practice problems, and an online component. 4. QuickMath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices. txt) or read online for free. George Polya is a Hungarian-American mathematics educator who believed that problem solving was an art and Quadratic Simultaneous Equations Instructions Use black ink or ball-point pen. 1) v2 + 2v − 8 = 0 2) k2 + 5k − 6 = 0 3) 2v2 − 5v + 3 = 0 4) 2a2 − a − 13 = 2 5) 2n2 − n Quadratic Equation. , for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the Here is the graph of this function: The graph just touches the x − axis at x = 2, so the function has a double root there. 23. Here is the graph of this function: The graph just touches the x − axis at x = 2, so the function has a double root there. Here you will find a range of worksheets to help you to learn to factorise a range of different quadratic equations 2. Find the GCF to factor. doc / . Based on the discriminant value, there are three possible conditions, which defines the nature of roots as follows:. Lesson 13. Quadratic Word Problems Short videos: Projectile Word Problem + 58. P m 7A 0lVl3 QrmiDgnhet usn nr0eXsXeirSv 0egdy. Printable in convenient PDF format. Here, we will solve different types of quadratic equation-based word problems. 0K) Answer Key - Chapter 02 (20. Solve by using the Quadratic Formula: \(4 a^{2}-2 a+8=0\). Analyze Quadratic Mr. Name (V10T9h Date Period I 3 4) (2m + + 3) = O Displaying top 8 worksheets found for - Gina Wilson Answer Key. So solving them are pretty simple and can be attempted by kids in grades 6-8. √8 √3 √6 3 Quadratic Equation in Standard Form: ax 2 + bx + c = 0; Quadratic Equations can be factored; Quadratic Formula: x = −b ± √(b 2 − 4ac) 2a; When the Discriminant (b 2 −4ac) is: positive, there are 2 real solutions; zero, there is one real III. x=y—5 13 . 3 Applications of Linear Equations; 2. 7. j j uA xl Fl H frzi Ngvh ntwsf 9r Desje Lrmv3eGdj. Let us learn here how to solve quadratic equations. 2, 3. Quadratic equations can be used in the same types of word problems as Name: _____Math Worksheets Date: _____ So Much More Online! Please visit: EffortlessMath. ALGEBRA. 2 Linear Equations; 2. Printable PDFs for Equations Worksheets for Grade 8. ) 14) a2 + 14a + 40 = 0 Solve the problem. Page 65: Additional Practice. A solution to such an Quadratic Exam 2 6. Solve by Graphing Worksheet and Review - To solve by graphing, the Using the Quadratic Formula Date_____ Period____ Solve each equation with the quadratic formula. On surface area worksheets Solving Equations: Exam Questions: Solving Equations: Solutions: Drawing Linear Graphs: Drawing Graphs: Solving Quadratics: Exam Questions: Solving Quadratics: Solutions: Where b 2-4ac is called the discriminant of the equation. Solve Quadratic Equations Using the Quadratic Formula. Answer : Since a is positive, Key Concepts. 8. (Total for question 1 is 5 Free math problem solver answers your algebra homework questions with step-by-step explanations. 4x 2 +9x = 12x. The Corbettmaths Practice Questions on Simultaneous Equations. 5-a-day Workbooks 2. 0K) Answer Key - Chapter 03 (44. Solving quadratic equations by factoring can be a daunting task for many students. IV. Since it has a negative y-intercept, c must be negative. Factoring Method. Solving Quadratic Equations – Using Quadratic Formula. Answer Tutor children using our printable quadratic equations worksheets. 19 of a grade on average - 0. 2nd grade social studies. Previous: Non-linear Simultaneous Equations Practice Questions Quadratic (2009) Grade 9 b. 12. x = 2 is the only solution to the equation. 4 Solve Quadratic Equations in Quadratic Form; 9. We can help you solve an equation of the form "ax 2 + bx + c = 0" Just enter the values of a, b and c below: The blue part (b 2 - 4ac) is called the "discriminant", solving problems, we can use Polya’s method introduced by George Polya. Answer \(a=\dfrac{1}{4}+\dfrac{\sqrt{31}}{4} i, \quad a=\dfrac{1}{4}-\dfrac{\sqrt{31}}{4} i\) We will see Answer(a)(i) [3] (ii) Solve 4x2 O 18x O 10 = 0. g b gM da Quadratic Equation Solver. The word quad is Latin for four or fourth, which is why a quadratic GRADE 9 Learning Module for Junior High School Mathematics 1 The learners will be able to: • solve quadratic equations by:(d) using the quadratic formula. Page 25: Additional Practice. ©J P230 u1i2 5 CK Auft QaT tSkotf 2tDwma7rzeB BL cL9Cz. Blank Quadratic Formula Notes. Otherwise, divide both sides of the equation by a. Lessons 6 (stop at 6:45) Lesson 8 (start at 6:50) Lessons 9-10. 8 seconds, is not half of 1. Triumph in your quadratic equations like never before! The zero-product property signifies that when the product of any two factors is 10. answer key. f(x) = x2 + 2x – Unit 4: Solving Quadratic Equations Homework 1: Solving Quadratcs by Graphing & Factoring Review ** This is a 2-page document ** Find the soluöons of each uadraäc equation by Free worksheet with answer keys on quadratic equations. I, II, IV and III C. Students will first learn about solving equations in A quadratic equation is an algebraic equation of the second degree in x. Writing Equations (GREAT PRACTICE!!!!) Writing Equations from Two Points; Grade 10 Quadratics Review Self-Test 1. 8 Answer: Height = 58. Answer \(x=-\dfrac{2}{3},x=\dfrac{1}{3}\) Key Concepts. docx), PDF File (. Solve By Factoring. 1 Solve Equations Using the Subtraction and Addition Properties of Equality; 2. A. 4 Equations With More Than One Variable; Chapter 16: Solving Quadratic Functions ANSWER KEY Study Guide Solving by Graphing: Graph the following without a calculator. mathematics quarter week. The quadratic equation in its standard form is ax 2 + bx + c = 0, where a and b are the coefficients, x is the variable, and Quadratic Formula Word Problems Answer Key and Lesson. There are several methods that we can use Solving Quadratics by Factorising How do I solve a quadratic equation using factorisation? Rearrange it into the form ax 2 + bx + c = 0. 2. If we get a radical as a solution, the final answer must have the radical in its simplified form. √8 √3 √6 3 Next: Adding Fractions Practice Questions GCSE Revision Cards. 5-a-day Workbooks To solve quadratic equations by factoring, we must make use of the zero-factor property. And best of all they all Chapter 16: Solving Quadratic Functions ANSWER KEY Study Guide Solving by Graphing: Graph the following without a calculator. x = {0, 3/4} x = {0, -3/4} x = {0, 4/3} no Using the Quadratic Formula Date_____ Period____ Solve each equation with the quadratic formula. The solution t ≈ 0. 3 Write the letter Learn how to solve quadratic equations by factoring with Khan Academy's step-by-step guide. Answer 32 63 5 8 0 3 26 35 0 (3 5) (7)0 35 0o r7 0 2 2 2 xx x xx xx xx Multiply both sides by x 8 2 . 717 , −8. It covers exponents, scientific notation, geometric transformations, linear equations, introduction to functions, linear The discriminant of a quadratic equation , is . no; Half of 11. To avail of the free version of 1. com Answers Solve quadratic inequalities 1) −1< T<1 2) −6< T<1 3) − 1-7 The Distributive Property 7-1 Zero and Negative Exponents 8-2 Multiplying and Factoring 10-2 Simplifying Radicals 11-3 Dividing Polynomials 12-7 Theoretical and Experimental Probability This document outlines a lesson plan on solving quadratic equations. Questions: Answers 1) x2 + 14x + 24 = 0 x = -3 or x = -7 2) x2 + 9x + GRADE 9 Learning Module for Junior High School Mathematics 1 The learners will be able to: • solve quadratic equations by:(d) using the quadratic formula. How do you solve quadratic equations in one variable quadratic? The way is given below to solve quadratic equations in one variable: 1. pdf), Text File (. In this module, you will learn how to solve word problems that involves quadratic equations. Here we will learn about the quadratic equation and how to solve quadratic equations using four methods: factorisation, using the quadratic equation formula, completing b. Answer the questions in the spaces provided — there may be more space than you 21) Explain two ways you could solve 20 = 5(−3 + x) -2- ©D 72 g061 U1Y 5K Uu Ptxat nSTozfHtKw4aDr Fe y yLzLpCJ. In solving quadratic equation that is not written in standard form, transform the equation in the standard form ax2 + bx + c = 0 where a, b, and c are real numbers and a ≠ 0 8 13) Use the quadratic formula to solve the equation. How does the graph of y = x 2 + 4 verify this fact? When does it make sense to use the graphing method for solving a quadratic equation? Review (Answers) Click Welcome to The Solving Quadratic Equations with Positive 'a' Coefficients of 1 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills. 45 more than those who didn't have the tutoring. Group all the Red Worksheet - Solve the following quadratics using the quadratic formula and match the question to the answer. Use the appropriate method to solve them: By Completing the Square; By Factoring; By Quadratic Find step-by-step solutions and answers to enVision Algebra 1 - 9780328931576, as well as thousands of textbooks so you can move forward with confidence. Start 7-day Extracting Square Roots. Section 8-1: Key Solving equations. If you solve by graphing, include a sketch. pg 215 #1-4. Then, check using your graphing calculator. The discriminant is found inside the square root of the quadratic formula. factoring review. The only quadratic with both of these is (4). Some of the worksheets for this concept are Quadratic equations, Solving one and two step equations • Student will apply methods to solve quadratic equations used in real world situations. Translate the facts into a system of linear equations. Lesson 1 (stop at 3:05) Lessons 2 - 4. 2(12) This document contains a 25-item summative test in mathematics for quarter 1. Are answer keys included? Yes! problems related to quadratic equations. Complete The Square. 3 Solve Then, we will look at 20 quadratic equation examples with answers to master the various methods of solving these typesof equations. Lesson 12. Here there is no constant term. In solving equations, we must always do the same thing to both sides of the equation. 4 Solve Equations in Quadratic Form; 9. Find the length of each side of the equilateral 1. 2 Solve Equations using the Division and Multiplication Properties of Equality; 2. The lesson begins with motivating students on the importance of solving quadratic equations to model real-world They all come with answer key solving quadratic equations by factoring worksheet answers too. There are many different Elementary Algebra Skill Solving Quadratic Equations by Factoring Solve each equation by factoring. . com. 9-4 Factoring to Solve Quadratic Equations 9-5 Completing the Square 9-6 The Quadratic Formula and the Discriminant 9-7 Linear, Quadratic, and Exponential Models 9-8 Systems of Completing the square – can be used to solve any quadratic equation. Download our sheets below: Worksheets topics. Solve a quadratic equation by finding square roots. 8 x − 20 x 2 = 0. Some of the worksheets for this concept are Factoring polynomials gina wilson work, Two step equations maze gina wilson Learn about quadratic functions and equations with videos, practice problems, and interactive exercises on Khan Academy. Page 21: Additional Practice. Example: 3x^2-2x-1=0. Example 9. This is true, of Once logged in, they can navigate to the desired resource or worksheet and locate the answer key section. pdf) or read online for free. 1 seconds. g. This product tackles this challenge head-on by providing a In math, a quadratic equation is a second-order polynomial equation in a single variable. Answer all questions. 1 - graphical solutions to quadratic equations. answer key *** extra practice *** 4. This math worksheet was created or last revised on 2019-11-25 This document outlines a lesson plan on solving quadratic equations. 8 m b. Quadratic Formula Notes Key. 3rd grade social studies. 582 , −4. 10 The New Committee Member’s Age. 1 Solving quadratic equations by factorisation Solve 32 63 5 8 0 2 2 xx x. Solve the system of equations using one of the methods in solving system of linear equations. The Chapter 16: Solving Quadratic Functions ANSWER KEY Study Guide Solving by Graphing: Graph the following without a calculator. 22. This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax 2 + bx + c = 0 for x, where a ≠ 0, using the There are different methods you can use to solve quadratic equations, depending on your particular problem. Grade 8 questions on quadratic equations with solutions and explanations included. 2 - solving quadratics by factoring. Find other quizzes for Mathematics and more on Quizizz for free! Solve the equation using the quadratic formula. Teacher-trusted tutoring Get your free solving equations worksheet of 20+ Here is a set of practice problems to accompany the Quadratic Equations - Part I section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Solving Quadratic Equations with Square Roots Date_____ Period____ Solve each equation by taking square roots. Kuta Software - Infinite Algebra 1 Solving Quadratic Equations by Factoring Solve each equation by factoring. Unit 8: Quadratic Equations Homework 12: Solving Quadratics by Method of Choice ** This is a 2-page document! ** Solve each equation by factoring, square roots, completing the square, or Solving Quadratic Equations: Worksheets with Answers Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. 4 Equations With More Than One Variable; Calculator Use. 1) The document contains a 40 item multiple choice test on 8 13) Use the quadratic formula to solve the equation. Week of April 20. It is Grade 9 Math Exam 1st FINAL - Free download as Word Doc (. Writing Equations (GREAT PRACTICE!!!!) Writing Equations from Two Points; Unit 8 - Solving Quadratic Equations. Show all your working and give your answers correct to two decimal The ultimate collection of free 8th grade math worksheets. Solve by 1) The document provides a sample test for a Grade 10 Standard Mathematics course. It is written in the form: ax^2 + bx + c = 0 where x is the variable, and a, b, and c are constants, a ≠ 0. 8 Solving Quadriatic Equations by Factoring. 6 meters is 5. Example 4. The answer key provides step-by-step solutions to the exercises, allowing 9. 6 Graphing Quadratic Equations—Vertex and Intercept Method. (Determine the y-intercept for the following equation: =− − ) + 2. Solve the equation for t when h = 0 . Find other quizzes for Mathematics and more on Quizizz for free! Use the quadratic formula to solve 2x 2 + 2x - 12. Here we will learn about the quadratic equation and how to solve quadratic equations using four methods: factorisation, using the quadratic equation formula, completing Analyze and Solve Systems of Linear Equations. The graph of problems related to quadratic equations. Find other quizzes for Mathematics and more on Quizizz for free! Solving Quadratic Equations quiz for 9th grade students. Choose "Solve Using the Quadratic Formula" from the topic selector and click to see the result in our Higher Worksheets Grades 1 to 9 Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Clicking on something like this will take you to the Grade 4 clip numbers and 7. M9AL-Ib-2. The test covers topics in quadratic equations including their standard form, discriminant, nature of roots, sum and product of roots, solving using factoring, Quadratics Equations Maze - Displaying top 8 worksheets found for this concept. Recall that a quadratic equation is in standard form if it is equal to 0: \[a x^{2}+b x+c=0\] where a, b, and c are real numbers and \(a\neq 0\). Find out how much you already know about quadratic 9. Answer(a)(ii) x = or x = [1] (b) Solve the equation 2x2 O 7x O 10 = 0. This worksheet will teach you how to solve quadratic problems Linear equations require students to work with a single variable of degree 1. Examples are then presented to illustrate how Solving Quadratic Equations quiz for 9th grade students. Solve a quadratic equation by completing the square. But what if the quadratic equation The quadratic equation x 2 + 4 = 0 has no real solutions. Solve quadratic equations by inspection (e. Click the links below to view the Student Answer Keys in Microsoft Word format. Graham's 8th Grade Algebra Website: Follow @MrGrahamMath on Twitter!! Home Writing Equations. (All solutions are real numbers. 5 Solve Solve Quadratic Equations of the Form x 2 + bx + c = 0 by Completing the Square. If the value of a = 1, proceed to step 2. Approximate values can be obtained using a calculator. Solve the equations following by factoring, using the quadratic formula or by graphing. 3 Write the letter Quadratic Formula and the Discriminant Answers Quadratic formula and the discriminant 1) 1 2) 8 3) −11 4) −15 5) 9 6) 40 7) 17 8) 60 9) −45 10) 57 11) 41 12) 60 13) 96 14) −7 15) 76 16) 189 Quadratic Equations quiz for 8th grade students. Challenge them to solve quadratic equations by applying methods such as factoring, completing the square, graphing, Unit 8 Test Study Guide Name: (Quadratic Equations) Date: Topic 1: Graphing Quadratic Equations (from Standard Form and Vertex Form) Graph each equation using a table of values. 0K) Introduction; 2. 5 c mathcentre August 7, Math Mammoth Grade 8 is a complete math curriculum for 8th grade. -2, 3. 1) m2 − 5m − 14 = 0 2) b2 − 4b + 4 = 0 3) 2m2 + 2m − 12 = 0 4) 2x2 − 3x − 5 = 0 5) These worksheets not only provide questions but also solutions in the form of answer keys. These are exact answers. Quadratic equations differ from linear equations by including a quadratic term with the variable raised to the second power of the form \(ax^{2}\). QuickMath Solve equations and Quadratic Equation. The lesson begins with motivating students on the importance of solving quadratic equations to model real-world problems. 2. Solving Quadratics Equations Using All Methods KEY - Free download as PDF File (. Round your answer to the nearest tenth, when appropriate. I, II, III, and IV B. In these cases, we may use a method for solving This is a copy of Mathematics 9 Q1 W2 Mod2 Solving Quadratic Equations for Grade 9 students, complete with lessons and examples. 7 Quadratic Word Problems: Age and Numbers. Since this is a quadratic function whose that opens upward, a must be positive. 582} 4) Quadratic Equation Grade 8 Worksheet – Quadratic equations can be solved with this Quadratic Worksheet. Find out how much you already know about quadratic Solving a Quadratic Equation Solve each equation by factoring or using the quadratic formula. Visit Mathway on the web. All of our 8th grade math worksheets are topic-specific, printable (they are available as pdf files), and include a complete answer Notes on Solving Equations, Inequalities and Absolute Value Key; Solving Equations, Inequalities, and Absolute Value (Review Day 2) Key; Videos: Solve Compound Inequalities; Solve Solve Quadratic Equations of the Form \(x^{2}+bx+c=0\) by Completing the Square. Mastering the quadratic formula is essential for solving many types of algebraic word problems. Solving the quadratic Key Point A quadratic equation takes the form Again we have two answers. Here you will learn about solving equations, including linear and quadratic algebraic equations, and how to solve them. 9 Age Word Problems. More Linear Equations Worksheets Graphing Linear Equations Worksheets Linear Name: Key Unit 4: Solving Quadratic Equations Date: Bell: Homework 7: The Quadratic Formula This is a document! Directions: Solve each equation the quadratic formula. 8 Construct a Learn how to solve quadratic equations by factoring with Khan Academy's step-by-step guide. Find the minimum value of the quadratic equation \(y=x^2+2x−8\). 1) k2 = 76 {8. Learning Target #4: Completing the Square. worksheet. 8t2 + 5. Lesson But solving quadratic equations like this is exactly what we have done earlier in this chapter. Math Gifs; Algebra; Siyavula's open Mathematics Grade 8 textbook, chapter 7 on Algebraic equations (Part 1) covering Solving equations by inspection the division on the left-hand side must produce the Mr. It is a very important method for rewriting a quadratic function in vertex form. The discriminant tells us the number and nature of the roots of the 2. Solving Equations and Inequalities. d i RM9a2d BeW iwti AtwhT tI 9nSf CiAnRimtZeu 9A Alig qelb 1rva u Improve your math knowledge with free questions in "Rewrite and solve quadratic equations" and thousands of other math skills. Page 67: Additional Practice. Steps in Solving Quadratic Equation by Completing the Square 1. This document contains mathematical equations and Quadratic Formula quiz for 9th grade students. 717} 2) k2 = 16 {4, −4} 3) x2 = 21 {4. This math worksheet Quadratic Simultaneous Equations Instructions Use black ink or ball-point pen. Page 63: Additional Practice. 2 Solve Quadratic Equations by Completing the Square; 9. Answer Key - Chapter 01 (23. two distinct real roots, if b 2 – 4ac > 0; two equal real 1. It tests students on topics from levels 1-2 up to 7-8 and includes 12 multiple choice questions testing Solving Quadratic Equations with Square Roots Date_____ Period____ Solve each equation by taking square roots. Clearly explain in words ALL of the transformations that must be applied to y = x2 to Name: _____Math Worksheets Date: _____ So Much More Online! Please visit: EffortlessMath. Solve a quadratic equation by using the Quadratic Formula. 582} 4) Next: Equations involving Fractions Practice Questions GCSE Revision Cards. Not all quadratic equations can be factored or can be solved in their original form using the square root property. Solve the following equation by factoring. Analyze Quadratic Quadratic Formula: x = − b ± b 2 − 4 a c 2 a. Read each question carefully before you start to answer it. Factorise.
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