HOW DO YOU SOLVE QUADRATIC - SOLVED EXAMPLES, EXERCISE

Please study
about Quadratic Equation before How Do You Solve Quadratic
if you have not already done so.

There, we gave introduction to Quadratic polynomial,
Quadratic Equation, Methods to solve the Quadratic
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

In Factoring of Trinomials (Quadratics), we follow the five steps.

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.

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

In Factoring of Trinomials (Quadratics) , we follow the five steps.

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.

Answers to Exercise : How Do You Solve Quadratic

1. -6, 5
2. 3⁄2, -2