Question

Which of the following is the complete list of roots for the polynomial function f (x) = (x squared + 2 x minus 15) (x squared + 8 x + 17)?

Answer 1

Answer:

x = -5, 3, -4 - i, -4 + i.

Step-by-step explanation:

(x^2 + 2x - 15)(x^2 + 8x + 17) = 0

(x^2 + 2x - 15) = 0

(x + 5)(x - 3) = 0

x = -5, 3.

x^2 + 8x + 17 = 0

Completing the square:

(x + 4)^2 - 16 = -17

(x + 4)^2 = -1

x + 4 = +/- i

x = -4 + i , -4 - i.