Find all values of a such that the given polynomial has three real roots
Source: Balkan MO ShortList 2007 A2
April 6, 2020
Problem Statement
Find all values of for which the polynomial
\begin{align*} f(x)=x^4-2x^3 + \left(5-6a^2 \right)x^2 + \left(2a^2-4 \right)x + \left(a^2 -2 \right)^2 \end{align*}
has exactly three real roots.