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.

Solution of Example 1 of How To Solve Quadratic Equations :

Factoring of the LHS of the Equation is shown below.

-*-*-*-*-*-*- Let P = 4 + x - 14x^{2} = -14x^{2} + x + 4

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

Step 1: Coefficient of x^{2} x constant term = -14 x 4 = -56

Step 2: We have to express -56 as two factors whose sum = coefficient of x = 1; -56 = 8 x (-7); [8 + (-7) = 1]

Step 3: P = -14x^{2} + x + 4 = -14x^{2} + 8x - 7x + 4

Step 4: P = 2x(-7x + 4) + 1(-7x + 4)

Step 5: P = (-7x + 4)(2x + 1)

Thus, By Factoring the Quadratic Polynomial, 4 + x - 14x^{2},we get the Factors as (-7x + 4)(2x + 1)

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

4 + x - 14x^{2} = 0 ⇒ (-7x + 4)(2x + 1) = 0 ⇒ (-7x + 4) = 0 or (2x + 1) = 0 (-7x + 4) = 0 ⇒ -7x = -4 ⇒ x = -4⁄-7 = 4⁄7 (2x + 1) = 0 ⇒ 2x = -1 ⇒ x = -1⁄2 Thus, x = 4⁄7, -1⁄2 are the two roots of the given Quadratic equation. Ans.

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