Find a polynomial with real coefficients that has zeros 3, 10i, and -10i.

Name: Find a polynomial with real coefficients that has zeros 3, 10i, and -10i.
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Question

Find a polynomial with real coefficients that has zeros 3, 10i, and -10i. ​

Quizplus · Accepted Answer

The polynomial with real coefficients that has zeros 3, 10i, and -10i is $(x-3)(x-10i)(x+10i)$. Simplifying this product gives $x(x^2+100)=\boxed{x^3+100x}$. This polynomial has real coefficients, and its zeros are 0, 10i, and -10i.

Find a Polynomial with Real Coefficients That Has Zeros 3