MathNet 2009-part-05 — 172 problems (EN–VI) Question 93

Let $P$ be a fourth degree polynomial, with derivative $P'$, such that $P(1) = P(3) = P(5) = P'(7) = 0$. Find the real number $x \neq 1, 3, 5$ such that $P(x) = 0$.