# Let P(x) be a real polynomial of degree ≤4 such that there are at least 5 distinct solutions to P(x) = 5. Find P(5). How???

$P \left(5\right) = 5$
A polynomial with degree $n \ge 1$ may attain a single value at most $n$ times. As $P \left(x\right)$ has at most degree $4$, but attains the value $5$ greater than $4$ times, the only way for this to be possible is if $P \left(x\right)$ is the constant function $P \left(x\right) = 5$.