I am given the following function $f : \mathbb R \mapsto \mathbb R, f(x) = x^4 – 4x + p\ \ \ $ and am asked to find $p$ such that $f$ has two identical real roots.
The proposed solution is to get the root from the relation $f(a) = f'(a) = 0$. What I'm curious about is when this relation is valid. It obviously isn't always valid (linear functions for example).
Best Answer
If $f$ has a double root at $x=a$, then $f(x)=(x-a)^2 g(x)$.