SOLUTION: Write a polynomial function f of least degree that has rational coefficients, a leading coefficients of 1, and the zeros 2, -3, and -3i.

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Question 1173983: Write a polynomial function f of least degree that has rational coefficients, a leading coefficients of 1, and the zeros 2, -3, and -3i.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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For such a polynomial, the roots are  2, -3, -3i  and  3i, including all complex conjugates,


so the polynomial is  


     p(x) = (x-2)*(x-(-3))*(x-(-3i))*(x-3i) = (x-2)*(x+3)*(x^2 + 9).

Solved, answered and explained.