Posted by **Jill** on Tuesday, July 26, 2011 at 9:57am.

write, in extended form, a polynomial(with real coefficients) of degree 3, with solutions 2,2-i.

- MATH -
**Reiny**, Tuesday, July 26, 2011 at 10:19am
complex roots always come in pairs, so if 2-i is a root, so is 2+i

using the sum and product of roots property of a quadratic,

sum of roots = 2-1 + 2+i = 4

product or roots = (2-i)(2+i) = 4 - i^2 = 5

so the quadratic part would be

x^2 - 4x + 5

the other factor would be x-2

so the polynomial is

(x-2)(x^2 - 4x + 5)

I will leave it up to you to expand it, if you need it in that form.

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