Consider the function f(x) = x2 + 2x - 15. what are the x-intercepts of the function?

x = - 5, x = 3

Step-by-step explanation:

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

x² + 2x - 15 = 0 ← in standard form

Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( + 2)

The factors are + 5 and - 3, since

5 × - 3 = - 15 and 5 - 3 = + 2, hence

(x + 5)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 ) ← x- intercept

x - 3 = 0 ⇒ x = 3 ⇒ (3, 0 ) ← x- intercept