Question

Show that the equation 2x^3-3x^2-2x+5=0 has a root between -1.5 and -1.

Answer 1

f(-1.5) = -11/2 and f(-1) = 2

f(x) is continuous on its domain.

thus by the intermediate value theorem, there must be a zero when -1.5<x<-1

Answer 2

Plot attached.