Never Judge a Problem by its Title
Algebra
Level
5
Let \(\displaystyle P\) and \(\displaystyle Q\) be two quadratic polynomials, such that \(\displaystyle P(z)=3z^2+4z+3\) and \(\displaystyle Q(z)=3z^2+6z+15\).
Furthermore, the product of \(\displaystyle P(x)\) and \(\displaystyle Q(y)\) for some \(\displaystyle x,y \in \mathbb{R}\) is \(\displaystyle 20\). Find their sum, ie, \(\displaystyle P(x)+Q(y)\).
It can be expressed as \(\displaystyle \dfrac{a}{b}\) for coprime positive integers \(\displaystyle a\) and \(\displaystyle b\). Find \(\displaystyle a+b\).
by
Satvik Golechha