if the equation z^2+az+ß=0 has a real root, prove that (aß*-ßa*)(a*-a)=(ß-ß*)^2\n* means conjugate
deshna jain , 10 Years ago
Grade
1 Answers
mycroft holmes
Last Activity: 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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