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if the equation z^2+az+ß=0 has a real root, prove that (aß*-ßa*)(a*-a)=(ß-ß*)^2 * means conjugate

if the equation z^2+az+ß=0 has a real root, prove that (aß*-ßa*)(a*-a)=(ß-ß*)^2
* means conjugate

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1 Answers

mycroft holmes
272 Points
10 years ago
Let m be the real root. Then we have m^2+am+b = 0 and taking conjugate, m^2+a* m + b* = 0 Subtracting, we get m (a-a*) = (b*-b) Substitute this value of m, and after some simple algebraic manipulations you arrive at the given equality

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