Answer: -5, 3, 4 + 1,4-i (option 2)
Step-by-step explanation:
The roots of an equation are the x values for f(x) = 0. Therefore to find the roots of the equation, you first set the function to 0 and then solve for the values of x.
since f(x) = -(x² + 2x - 15) (x² + 8x + 17)
0 = -(x² + 2x - 15) (x² + 8x + 17)
∴ either -x² - 2x + 15 = 0 OR x² + 8x +17 = 0
when -x² - 2x + 15 = 0
-x² - 5x + 3x + 15 = 0
(x - 3 ) (-x - 5) = 0
⇒ x = 3 or x = -5
when x² + 8x +17 = 0
= 0 OR
= 0 (using the quadratic equation)
⇒ x = 4 + i or x = 4 - i
∴ the complete list of roots is -5, 3, 4 + 1,4-i (option 2)