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butalik [34]
2 years ago
7

If 2i is a zero of f(x)=x^4+x^2+a, find the value of a

Mathematics
1 answer:
Sedbober [7]2 years ago
5 0

By the polynomial remainder theorem, because <em>x</em> = 2<em>i</em> is a zero of <em>f(x)</em>, we have no remainder upon dividing <em>f(x)</em> by <em>x</em> - 2<em>i</em>.

Computing the quotient yields

\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}

Then if the remainder term is 0, follows that <em>a</em> = -12.

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