If the Quadratic equation αx2 + βx + a2 + b2 + c2 ab bc ca = 0 has imaginary roots, then Prove that 2(α β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0
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Just to clear things up, do you mean: $\displaystyle ax^2+\beta x+a^2+b^2+c^2-ab-bc-ac=0$ Prove that: $\displaystyle 2(a-\beta)+(a-b)^2+(b-c)^2+(c-a)^2<0$? Next time you want to show powers use the '^' symbol. e.g $\displaystyle 2^n$ is 2^n.
Originally Posted by nsprasad2001 If the Quadratic equation αx2 + βx + a2 + b2 + c2 ab bc ca = 0 has imaginary roots, then Prove that 2(α β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0 The descriminant has to be negative. RonL
Yes
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