Find 4th Degree Polynomial?

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mattimeo_boyd Posts: 31, Reputation: 1

Junior Member

#1

Jun 5, 2010, 11:26 AM

Find 4th Degree Polynomial?

How do you find a 4th degree polynomial with integral coefficients that has zeros of 2 ( multiplicity of 2) and -i?

galactus Posts: 2,271, Reputation: 282

Ultra Member

#2

Jun 5, 2010, 03:23 PM

You know the roots. 2 occurs twice as root. If -i is a root, so is i.

Therefore, we have

$(x-2)^{2}(x+i)(x-i)=0$

But $(x+i)(x-i)=x^{2}+1$

So, the resulting quartic polynomial is

$(x-2)^{2}(x^{2}+1)$

Expand out to find the polynomial .

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