Question 12
Consider the polynomial
$$
p(x) = (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a)
$$
Prove that $p(x) \geq 0$ for every $x \in \mathbb{R}$ if and only if $a = b = c$.
$$
p(x) = (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a)
$$
Prove that $p(x) \geq 0$ for every $x \in \mathbb{R}$ if and only if $a = b = c$.