Please help soon. Due tomorrow. Can anyone help me create a polynomial function with given zeros?

The zeros are 2, 4 + i, 4 - i

The i is imaginary

I can get this far:

(x-2)(x-4+i)(x+4-i)

But I'm confused with the signs for the second and third sets of parenthesis. I'm not sure what signs are supposed to change or if I have them correct.

1 Answer
Jim H
Dec 5, 2016

The zeros are 2, and 4+i and 4−i

The factors are:
(x−2), (x−(4+i)), , and (x−(4−i))

I would start by multiplying

(x−(4+i))(x−(4−i))=x2−x(4−i)−x(4+i)+(4+i)(4−i)

=x2−4x+xi−4x−xi+(16−i2)

=x2−8x+(16−(−1))

=x2−8x+17

Note that I used the product of a sum and difference (4+i)(4−i)=16−i2. You can multiply htis out in more detail is you like.

Now multiply (x−2)(x2−8x+17) to get

x3−8x2+17x−2x2+16x−34

=x3−10x2+33x−34

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