# Inspired by Dev Sharma.

Algebra Level 5

$$f(x)$$ is a monic quadratic polynomial such that $$f(1)=7+b$$ and $$f(2)=16+b$$.

And $$p(x)$$ is another monic quadratic polynomial such that $$p(1)=4+b$$ and $$p(2)=7+2b$$.

If $$f(x)$$ and $$p(x)$$ have a root in common then find the product of all possible values of $$b$$.

Let $$x$$ be the answer, then submit it as $$\left | x \right |$$.

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