since you're given with the zeros of the function then you will the idea that
x = 3/2 ; x = -2
having it equated into zero, you'll have it as:
x - 3/2 = 0; x + 2 = 0
or the factors would be
(x - 3/2)(x + 2) = 0
x² + 2x - 3/2x - 3 = 0
x² + 1/2 x - 3 = 0
multiplying the whole equation with 2 to remove the fraction you'll have
2x² + x - 6 = 0
therefore
f(x) = 2x² + x - 6
