Applying the rational roots theorem because of the -9 and 4, -3/2 looks like a good bet because -3 is a factor of -9 and 2 is a factor of 4.
Plugging x = -3/2 into the function we have
4(-3/2)^4 + 8(-3/2)^3 - 7(-3/2)^2 - 21(-1.5) - 9 = 0
so -3/2 is a zero
x = 1 and x = -3/4 are not zeroes.
