Question

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???

Answer 1

`P(5) = 5`

Explanation:

A polynomial with degree `n>=1` may attain a single value at most `n` times. As `P(x)` 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(x)` is the constant function `P(x) = 5`.