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
Solve x2 + x - 30 = 0.
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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