tmua.me Tau Paper 1 · Question 14

tmua.me papers

tmua.me Tau Paper 1 · Q14

Paper 1AlgebraFunctions & graphs

For real numbers $a,b$ , let

P(x)=(x^2+1)^3+ax(x^2+1)^2+bx^3.

Suppose that $P(1)=0$ and $P(x)\ge0$ for every real $x$ . Also suppose that $P(x)=P(-x)$ has exactly five distinct real solutions.

What is the least possible sum of the squares of these five solutions?

6

\dfrac{28}{3}

8

\dfrac{20}{3}

12

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