examday

/TMUA

In this question, $f(x)$ is a non-constant polynomial, and $g(x)=xf'(x)$.

$f(x)=0$ for exactly $M$ real values of $x$.

$g(x)=0$ for exactly $N$ real values of $x$.

Which of the following statements is/are true?

• I. It is possible that $M<N$.
• II. It is possible that $M=N$.
• III. It is possible that $M>N$.