How do you write a polynomial function of least degree given the zeros -1, 2i?

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Answer 1 · 2016-11-15T21:01:21

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The zero at -1 implies that (x + 1) is a factor:

#y = (x + 1)#

The zero at 2i implies that (x - 2i) is a factor.

#y = (x + 1)(x + 2i)#

The zero at 2i implies that -2i is, also, a zero and, therefore, (x + 2i) is a factor.

#y = (x + 1)(x + 2i)(x - 2i)#

We know that the product of complex conjugates #a +- bi# always produce #a^2 + b^2#

#y = (x + 1)(x^2 + 4)#

Use the F.O.I.L method to multiply:

#y = x^3 + 4x + x^2 + 4#

Rearrange in descending power:

#y = x^3 + x^2 + 4x + 4#