# HOW DO YOU SOLVE QUADRATIC - SOLVED EXAMPLES, EXERCISE

if you have not already done so.

There, we gave introduction to Quadratic polynomial,
Equations and about Method of Solving by Factoring.

That knowledge is a prerequisite here.

Here, we apply the Method to solve problems.
Solved Examples and Exercise problems are given.

## Example 1 : How Do You Solve Quadratic

Solve x2 + x - 42 = 0.

Solution of Example 1 How Do You Solve Quadratic :

The Factoring of the LHS of the above Equation is given below.

-*-*-*-*-*-*
Let P = x2 + x - 42

Step 1: Coefficient of x2 x constant term
= 1 x -42 = -42

Step 2: We have to express -42 as two factors whose sum
= coefficient of x = 1 ;
-42 = -6 x 7; (- 6 + 7 = 1)

Step 3: P = x2 + x - 42 = x2 + 7x - 6x - 42

Step 4: P = x(x + 7) - 6(x + 7)

Step 5: P = (x + 7)(x - 6)

Thus, By Factoring the Quadratic Polynomial, x2 + x - 42,we get the Factors as (x + 7)(x - 6)

-*-*-*-*-*-*

x2 + x - 42 = 0 ⇒ (x + 7)(x - 6) = 0
⇒ (x + 7) = 0 or (x - 6) = 0
(x + 7) = 0 ⇒ x = -7
(x - 6) = 0 ⇒ x = 6
Thus, x = -7, 6 are the two roots of the given Quadratic equation. Ans.

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## Example 2 : How Do You Solve Quadratic

Solve 12 - 4x - 5x2 = 0.

Solution of Example 2 of How Do You Solve Quadratic :

The Factoring of the LHS of the above Equation is given below.

-*-*-*-*-*-*
Let P = 12 - 4x - 5x2 = -5x2 - 4x + 12

Step 1: Coefficient of x2 x constant term
= -5 x 12 = -60

Step 2: We have to express -60 as two factors whose sum
= coefficient of x = -4 ;
-60 = -10 x 6; (-10 + 6 = 4)

Step 3: P = -5x2 - 4x + 12 = -5x2 - 10x + 6x + 12

Step 4: P = -5x(x + 2) + 6(x + 2)

Step 5: P = (x + 2)(-5x + 6)

Thus, By Factoring the Quadratic Polynomial, 12 - 4x - 5x2,we get the Factors as (x + 2)(-5x + 6)

-*-*-*-*-*-*

12 - 4x - 5x2 = 0 ⇒ (x + 2)(-5x + 6) = 0
⇒ (x + 2)= 0 or (-5x + 6) = 0
(x + 2) = 0 ⇒ x = -2
(-5x + 6) = 0 ⇒ -5x = -6 ⇒ x = -6⁄-5 = 6⁄5
Thus, x = -2, 6⁄5 are the two roots of the given Quadratic equation. Ans.

## Exercise : How Do You Solve Quadratic

1. Solve x2 + x - 30 = 0.
2. Solve 6 - x - 2x2 = 0.

For Answers See at the bottom of the Page.

NOTE: You may solve all these problems of Exercise
using Quadratic Formula, after learning it.

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1. -6, 5
2. 3⁄2, -2

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