tmua.me Tau Paper 1 · Question 10

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tmua.me Tau Paper 1 · Q10

Paper 1Functions & graphsSequences & seriesAlgebra

Let $a$ be real and $f(x)=x^2-ax$ . Define

f_1(x)=f(x),\qquad f_{n+1}(x)=f\bigl(f_n(x)\bigr)\quad(n\ge1).

Suppose that $f_2(x)=0$ has four distinct real roots which, in increasing order, form an arithmetic progression.

Which set contains exactly the possible numbers of distinct real roots of $f_5(x)=0$ ?

\{12,32\}

\{8,32\}

\{10,16\}

\{16,32\}

\{10,32\}

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