This document discusses four methods for solving quadratic equations: factorization, completing the square, using a formula, and using graphs. It provides an example of solving the equation 2x^2 - 10x + 12 + x^2 + 6x = -9 by factorizing into (x - 3)(x - 1) = 0, finding that the solutions are x = 3 or x = 1.

1. This unit is about the solution of quadratic equations.. We will look at four methods: solution by factorization, solution by completing the square, solution using a formula, and solution using graphs Contents 1. Introduction 2. Solving quadratic equations by factorization 3. Solving quadratic equations by completing the square 4. Solving quadratic equations using a formula 5. Solving quadratic equations by using graphs solving quadratic equation

2. 1. Introduction This unit is about how to solve quadratic equations. A quadratic equation , in mathematics, any second-degree polynomial equation. Factorisation and use of the formula are particularly important. Example Suppose we wish to solve 2 x 2 − 10 x −12 + x 2 +6x = −9 We begin by writing this in the standard form of a quadratic equation by subtracting 9 from each side to give x 2 − 10 x −12 + x 2 +6x+9 = 0

3. We factorize the quadratic by looking for two numbers which multiply together to give 6, and add to give − 5. Now − 3 ×− 2 = 6 − 3 + − 2 = − 5 so the two numbers are − 3 and − 2. We use these two numbers to write − 5 x as − 3 x − 2 x and proceed to factorize as follows: 2x 2 − 10 x +12 + x 2 +6x+9=0 (2x 2 − 10 x +12) +( x 2 +6x+9)=0 2( x 2 − 5 x +6) +( x − 3) =0 (x 2 − 3 x − 2 x +6)+( x − 3) = 0 . 2 x ( x − 3) − 2( x − 3) +( x − 3) = 0 ( x − 3) ( x − 2) +( x − 3) = 0 ( x − 3)(( x − 2) +1) ( x − 3) ( x − 1 ) =0

4. from which (x − 3) = 0 ( x − 1 ) = 0 so that x = 3 or x = 1 equating each factor to zero

5. These are the two solutions. possible answers x = 3 or x = 1 Note : it is possible that your answer may be same but it may be different whenever you get square ”2” and no other digit your answer is same

6. MADE BY HIRA TUFAIL