Question 16
The polynomial $x^3 + px + q$, where $p$ and $q$ are real numbers and at least one of them is non-zero, has a real root $a$ that satisfies
$$
a^2 \le -\frac{4}{3}p.
$$
Prove that this polynomial has a real root different from $a$.
$$
a^2 \le -\frac{4}{3}p.
$$
Prove that this polynomial has a real root different from $a$.