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# Polynomials

You'll make Vieta proud.

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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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