Posted by **Tim** on Thursday, March 10, 2011 at 5:29pm.

Find the polynomial function P of the lowest possible degree, having real coefficients, with the given zeros.

3+2i, -2 and 1

- Algebra-zeroes -
**MathMate**, Friday, March 11, 2011 at 10:14am
The zeroes of polynomials are either real or complex. Complex zeroes always come in with the conjugates.

Since the three zeroes above do not include conjugates, the minimum degree of polynomial is 3+1=4.

The polynomial having zeroes of

3+2i, -2, 1

and the conjugate 3-2i is therefore

P(x)=(x-(-2))(x-1)(x-3-2i)(x-3+2i)

=(x+2)(x-1)(x²-6x+13)

Expand if necessary

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