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 \(\left | x \right |\).

This problem is original.

: Inspiration

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