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Balkan MO Shortlist
2007 Balkan MO Shortlist
A2
A2
Part of
2007 Balkan MO Shortlist
Problems
(1)
Find all values of a such that the given polynomial has three real roots
Source: Balkan MO ShortList 2007 A2
4/6/2020
Find all values of
a
ā
R
a \in \mathbb{R}
a
ā
R
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.