tmua.me Tau Paper 1 · Question 19

A monic polynomial of degree $12$ has twelve distinct real roots, none equal to $0$ or $1$ . Replacing every root $r$ by $1-r$ leaves the set of roots unchanged; so does replacing every root $r$ by $1/r$ .

The sum of the squares of the twelve roots is $30$ . Let $T$ be the sum of their fourth powers.

Which one of the following describes all the possible values of $T$ ?

174<T\le\dfrac{777}{4}

174\le T\le\dfrac{777}{4}

174<T<\dfrac{777}{4}

T>174

174\le T<\dfrac{777}{4}

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tmua.me Tau Paper 1 · Q19