Question 431581: I am on break and can't get help from my math teacher, I need to answer a question using these two functions f(x)=x^5-x^4+40x^2-x-39 and h(x)=2x^4+7x^3-3x^2-14x-6
How many roots do f(x) and h(x) each have in the complex numbers? Help is greatly appreciated.
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! in general, using the fundamental theorem of algebra, you can conclude that any polynomial of degree n has n solutions (including multiplicity(order)) of the roots.
ex: g(x) = x^2 + 1. This has no solutions in real numbers, but by the fund thm of algebra, they have 2 solutions in complex numbers; namely x=i and x=-i, where i = sqrt(-1)
ex: p(x) = x^2+2i+1. This has 1 solution in the complex numbers, x=i, but it has order 2, therefore it satisfies the fund thm of algebra
can you now name how many solutions your functions will have in complex numbers?
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