(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that f(x) is a polynomial of degree n with real coefficients; that is,

f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real)

Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x)

2. Relevant equations

(a+bi)*(a-bi) = a^2 + b^2 where a, and b are always reals?

Not really sure if this helps or not.

3. The attempt at a solution

I'm really clueless on how to start approaching this. I was thinking perhaps the fundamental theorem of algebra might be of some use, or perhaps the fact that a number of complex form multiplied by it's conjugate is a real number, but I'm really not sure.

Could anyone give me a nudge in the right direction?

Any help would be greatly appreciated!! Thanks!

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# Show that complex conjugate is also a root of polynomial with real coefficients

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