Is x 32 a zero of the function fx 2x3 7x2 8x 3 Explain

Is x = -3/2 a zero of the function f(x) = 2x3 + 7x2 - 8x + 3? Explain your answer!

Solution

if x =-3/2 is the zero of polynomial then f(-3/2)=0

f(-3/2)

= 2(-3/2)³ + 7(-3/2)² - 8(-3/2) + 3

=(-54/8)+(63/4)+(24/2) +3

=(-27/4)+(63/4)+12+3

=(36/4)+15

=9+15

=24

0

so x = -3/2 is not a zero of the function f(x) = 2x3 + 7x2 - 8x + 3