Posted by **Mary** on Thursday, September 22, 2011 at 7:53pm.

Form a polynomial, f(x) with real coefficients having the given degree and zeros. Degree: 4 ; Zeros: 4i and 5i

Really need help! don't know where to start.

- Calculus -
**Steve**, Friday, September 23, 2011 at 1:14pm
Review the properties of polynomials with real coefficients. If they have complex roots, the roots appear in conjugate pairs. So, since you have roots 4i and 5i, the other roots are -4i and -5i.

Recall that x^2 + a^2 = (x-ai)(x+ai)

So, your polynomial is (x^2+16)(x^2+25) = x^4 + 41x^2 + 400

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