Answer
$-1, -4, -1 + i\sqrt 6, -1 - i\sqrt 6$
Work Step by Step
This question asks for ALL zeros of the function
Given $P(x) = x^4 + 7x^3 + 9x^2 - 17x - 20$
See image below for synthetic division
So x = -1, -4 is a zero
Factor and set P(x) = 0
$x^2 + 2x - 5$
$x^2 + 2x + 1 = 6$
$(x+1) ^ 2 = 6$
$x = -1 +/- i\sqrt 6$
Thus the solutions are $-1, -4, -1 + i\sqrt 6, -1 - i\sqrt 6$
