Question 53
Let $p,q$ be real numbers and consider the cubic equation
$$
x^{3}+p x+q=0
$$
a) If $x_0$ is a real root, then
$$
x^{3}+p x+q=\left(x-x_{0}\right)\left(x^{2}+a x+b\right)
$$
Verify that $a=x_0$.
b) Verify that $p^2\ge4x_0q$.
$$
x^{3}+p x+q=0
$$
a) If $x_0$ is a real root, then
$$
x^{3}+p x+q=\left(x-x_{0}\right)\left(x^{2}+a x+b\right)
$$
Verify that $a=x_0$.
b) Verify that $p^2\ge4x_0q$.