Answer
$3i, -3i, i\sqrt6, -i\sqrt6$
Work Step by Step
This question asks for ALL zeros of the function
Given $P(x) = x^4 + 15x^2 + 54$
Factor and set $P(x) = 0$
$(x^2 + 6) (x^2 + 9)$
$x^2 + 9 = 0$
$x = +/- 3i$
$x^2 + 6 = 0$
$x = +/- i\sqrt6$
$x = 3i, -3i, i\sqrt6, -i\sqrt6$
Thus the solutions are $3i, -3i, i\sqrt6, -i\sqrt6$