Examine the number of sign changes for f(x) and f(-x)
[tex] f\left(x\right)=-x^3-x^2+14x-24 [/tex]
[tex] (-) (-) (+) (-) [/tex]
There are two sign changes for the coefficient of f(x), so the function has 2 or 0 positive real zeros.
[tex] f(-x)= x^3-x^2-14x-24 [/tex]
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
