Question

Find the zeros of the function f(x) = x2 +9x + 20 by factoring.

Answer 1

Let a and b be the factors of the expression such that x² + 9x + 20 = (x + a)(x + b). The sum of a and b is the numerical coefficient of the second term and their product is the constant.
                                 a + b = 9               ;  a = 9 - b
                                 ab = 20                 ; (9 - b)(b) = 20
The value of a and b are 4 and 5. The factors are therefore,
                                    (x + 4)(x + 5) 
To find the zero, equate the factors to zero which yields an answer equal to x = -4 and x = -5.