Equations and polynomials?

Algebra Level 5

Let \(a, b, c, d, e\) be real numbers that satisfy the equations:

\(c+a=15\)

\(ac+b+d=85,\)

\(ad+bc+e=225,\)

\(ae+bd=274,\)

\(be=120.\)

Find the sum of all possible values of \(e\).

Here's a hint (a simpler problem)

This problem is part of the set ... and polynomials

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