THIS USER ASKED 👇

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)?

A) 5, 3
B)–5, 3, –4 + i, –4 – i
C)–5, 3, –4 + i, 4 + i
D) –4 + i, –4 – i

THIS IS THE BEST 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.