OMCC 2016 Problem 3

The polynomial $Q(x)=x^3-21x+35$ has three different real roots. Find real numbers $a$ and $b$ such that the polynomial $x^2+ax+b$ cyclically permutes the roots of $Q$ , that is, if $r$ , $s$ and $t$ are the roots of $Q$ (in some order) then $P(r)=s$ , $P(s)=t$ and $P(t)=r$ .