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Quadratic Equation Factorization Method
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You know how to factorize quadratic and other simpler polynomials. Here you'll learn how to apply the method of factorization to solve simple quadratic equations.

Say quadratic equation ax2 + bx + c = 0; a 0.

Let the quadratic polynomial ax2 + bx + c be expressed as the product of two linear factors. E.g. (px + q) and (rx + s), where p, q, r, s are real numbers such that p 0 and r 0. Then,
ax2 + bx + c = 0
(px + q) (rx + s) = 0
px + q = 0 or, rx + s = 0

When you solve these linear equations, the possible roots of the given quadratic equation you'll get are:
                                  x = -(q/p) and x = -(s/r)
People who saw this lesson also found the following lessons useful:
Rational Expressions - Addition
Determining the Nature of the Roots
Factorization and Factor Theorem
Elimination by Substitution Method
Example: Solve the following quadratic equations by factorization method:
(i) x2 + 6x + 6                                 (ii) x2 + 22x - 6 = 0

Solution
(i) Given:
x2 + 6x + 5 = 0
x2 + 5x + x + 5 = 0
x(x + 5) + (x + 5) = 0
(x + 5)(x + 1) = 0
x + 5 = 0 or x + 1 = 0
x = -5 or x = -1
Thus, x = - 5 and x = - 1 are two roots of the equation x2 + 6x + 5 = 0.

(ii) Given:
x2 + 22x - 6 = 0
x2 + 32x - 2x - 6 = 0
x(x + 32) - 2(x + 32) = 0
(x + 32)(x - 2) = 0
x + 32 = 0 or x - 2 = 0
x = -32 or x = 2
Thus, x = -32 and x = 2 are two roots of the given equation.
 
   
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