Rolle's theorem with odd function

Question

If I have some cubic equation $f(x)$, and I need to find how many solutions $f(x)$ has. $f'(x)$ has two zeros, does it state that $f(x)$ has $3$ solutions by Rolle's theorem?

$$f(x)= x^3+2x^2-7x+1$$

Answer 1

If $f'(x )=0$ for $x=\alpha , \beta$ and $$f(\alpha) \cdot f(\beta) \le 0$$ Then $f(x)=0$ has three real roots.