How do you write a polynomial with zeros 3i, -3i, 5 and leading coefficient 1?

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Answer 1 · 2016-11-17T20:05:52

Please see the explanation.

The leading coefficient is 1:

y = 1

Multiply by the factor corresponding to the root #3i#:

#y = (x - 3i)#

Multiply by the factor corresponding to the root #-3i#:

#y = (x - 3i)(x + 3i)#

Multiply by the factor corresponding to the root 5:

#y = (x - 3i)(x + 3i)(x - 5)#

When we multiply an complex conjugate pair #(a +- b)#, we know that we get the sum of 2 squares #(a^2 + b^2)#:

#y = (x^2 + 9)(x - 5)#

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

#y = x^3 - 5x^2 + 9x - 45#