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 x^{2} + 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 = x^{2} + x - 42

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

Step 1: Coefficient of x^{2} 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 = x^{2} + x - 42 = x^{2} + 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, x^{2} + x - 42,we get the Factors as (x + 7)(x - 6)

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

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

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

12 - 4x - 5x^{2} = 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

Solve x^{2} + x - 30 = 0.

Solve 6 - x - 2x^{2} = 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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