Answer
$[-2, -3/2] U [3/2, 2]$
Work Step by Step
$4x^4 - 25x^2 + 36 \leq 0$
Find the roots of the function
$(x^2 - 4) (4x^2 - 9)$
$(x^2 - 4) 4(x^2 - 9/4)$
$4(x+2)(x+3/2)(x-3/2)(x-2)$
$x = -2, -3/2, 3/2, 2$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -2] $(-)(-)(-)(-) = (+)$
[-2, -3/2] $(+)(-)(-)(-) = (-)$
[-3/2, 3/2] $(+)(+)(-) (-) = (+)$
[3/2, 2] $(+)(+)(+)(-) = (-)$
[2, ∞) $(+)(+)(+)(+) = (+)$
Thus the solution is $[-2, -3/2] U [3/2, 2]$
