Question

State the possible number of positive real zeros, negative real zeros, and imaginary zeros
f(x)=-x^3-x^2+14x-24

Answer 1

Examine the number of sign changes for f(x) and f(-x)

$f\left(x\right)=-x^3-x^2+14x-24$

$(-) (-) (+) (-)$

There are two sign changes for the coefficient of f(x), so the function has 2 or 0 positive real zeros.

$f(-x)= x^3-x^2-14x-24$

There is 1 sign change for the coefficients of f(-x). So f(x) has one negative real zero.

Thus, f(x) has 2 or 0 positive real zeros, 1 negative real zero, 2 or 4 imaginary zeros