SOLUTION: true or false: given that 4i is a zero of f(x)=x^4+13x^2-48, there must be three real zeros of f(x)?

SOLUTION: true or false: given that 4i is a zero of f(x)=x^4+13x^2-48, there must be three real zeros of f(x)?

Algebra.Com

Question 919884: true or false:
given that 4i is a zero of f(x)=x^4+13x^2-48, there must be three real zeros of f(x)?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
False

-4i must necessarily be a root. By fundamental thm. of algebra, f has exactly four complex roots (including multiple roots) so f has at most two real roots.
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