Question

Algebraically determine the zeros of the quadratic function g(x)= x^2+7x+12. Show all work please

Answer 1

Answer:

x = - 4, x = - 3

Step-by-step explanation:

To find the zeros equate f(x) to zero, that is

x² + 7x + 12 = 0

To factorise the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

The factors are + 4 and + 3, since

4 × 3 = 12 and 4 + 3 = 7, hence

(x + 4)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 3 = 0 ⇒ x = - 3