# 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.

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