Let be a quadratic polynomial function of with two different roots and . Given that a branch of of the square root of exists in a domain , demonstrate that neither nor can belong to . If had a double root, would the analogous statement be true?

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- Nov 26th 2011, 12:35 PMtarheelbornComplex analysis -pth roots
Let be a quadratic polynomial function of with two different roots and . Given that a branch of of the square root of exists in a domain , demonstrate that neither nor can belong to . If had a double root, would the analogous statement be true?

- Nov 29th 2011, 05:12 PMtarheelbornRe: Complex analysis -pth roots
I know that and I know that . So if has two different roots, then how could which implies that and and are all in . Is that where I need to go?