Question

Which of the following is a rational zero of the function

Answer 1

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.