# 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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