Question 40
Consider the real sequences $(a_n)_{n \ge 1}$, $(b_n)_{n \ge 1}$, $(c_n)_{n \ge 1}$. Prove that if the sequence
$$
p_n(x) = (x - a_n)(x - b_n)(x - c_n)
$$
converges for infinitely many values of $x$, then it converges for every $x \in \mathbb{R}$.
$$
p_n(x) = (x - a_n)(x - b_n)(x - c_n)
$$
converges for infinitely many values of $x$, then it converges for every $x \in \mathbb{R}$.