# Subharthi's progression

**Algebra**Level 3

The four numbers \(c<d<e<f\) are 4 consecutive terms of a geometric progression. It is given that \(c\) and \(d\) are the roots of \(x^2-3x+a=0\), and that \(e\) and \(f\) are the roots of \(x^2-12x+b=0\). What is the value of \(a+b\)?

This problem is posed by Subharthi C.