Give an example of a polynomial of degree 5, whose only real roots are *x*=2 with multiplicity 2, and *x*=-1 with multiplicity 1.

We need factors of the form and (*x*+1) to satisfy the root requirements. We also know that the last 2 of the 5 roots of the polynomial have to be complex; so, for instance, will do:
The polynomial

satisfies all the requirements.

**N.B.: ** In problems like this one, do not bother to multiply out. You were just asked to write down a polynomial with certain properties; nobody told you to write down the polynomial in a particular form.

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*Helmut Knaust *

Tue Jun 24 09:53:41 MDT 1997

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