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Polynomials

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Let \(f(x)=x^4-7x^3-3x+10\). How many negative numbers \(a\) are there such that \(f(a)=0\)?

Steve has a calculator that only has one operation. When given a number, the calculator adds 6 to it. Jordan similarly has a calculator that does one thing: it takes a number and squares it.

Alice gives Steve a number \(a\). Steve plugs \(a\) into his calculator and gives the result to Jordan who plugs it into his calculator. He gives Alice the result. Similarly, Adam gives another number \(b\) to Steve who computes it, passes the result to Jordan, who computes it and gives the result to Adam. If Alice and Adam both got the same number back and \(a\neq b\), what is \(a+b\)?

What are the sum of the roots of the polynomial \[f(x)=x^2-5x+6?\]

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