# Minimum polynomial

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• Jan 26th 2008, 10:30 AM
tttcomrader
Minimum polynomial
Let $w = \frac {-1}{2} + \frac {3^{1/2}}{2}i$

Find the minimum polynomial for w over Q.

I know that the minimum poly is the monic function f such that f(w) = 0.

Nevermind, guys, I finally got the answer, is it p(x) = x^2 + x + 1?

It looks so easy now, but it took me so long to get it. Thanks.
• Jan 26th 2008, 02:12 PM
ThePerfectHacker
Quote:

Originally Posted by tttcomrader
Let $w = \frac {-1}{2} + \frac {3^{1/2}}{2}i$

Find the minimum polynomial for w over Q.

I know that the minimum poly is the monic function f such that f(w) = 0.

Nevermind, guys, I finally got the answer, is it p(x) = x^2 + x + 1?

It looks so easy now, but it took me so long to get it. Thanks.

The thing you do it write $w = -\frac{1}{2} + i\frac{\sqrt{3}}{2}$ and square both sides and bring it to a form of a polynomial having rational coefficients.