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On this link is a question about functions.

My question is, in that question itself, a pivotal part of the solution is to realise that the discriminant of the (positive) discriminant is negative. Could someone please tell me why that is so?

Thanks.

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The discriminant of the quadratic equation $ax^2+bx+c=0$ is given by $b^2-4ac$. It is easily seen from the quadratic formula (which can be proved by completing the square) that the discriminant is less than zero, then the solutions are imaginary.

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  • $\begingroup$ The quadratic formula and its proof can be found on wikipedia $\endgroup$ – Beans on Toast Aug 1 '15 at 20:29
  • $\begingroup$ I am perfectly aware of the quadratic formula and what the discriminant is. My question is about the discriminant of the discriminant. Could you please rephrase your answer after you look at the link? Thanks. $\endgroup$ – coolcheetah Aug 1 '15 at 20:34
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    $\begingroup$ I think you need to rephrase your question posted here before going any further. There is no such thing as the " discriminant of the discriminant " , as you put it. You can only have a discriminant with respect to an equation. So it's difficult to ascertain what you are asking for. $\endgroup$ – Beans on Toast Aug 1 '15 at 22:03
  • $\begingroup$ Sorry for the confusion. I meant to say that the question that I mentioned had a discriminant which was a quadratic equation in itself. And it had a negative discriminant. $\endgroup$ – coolcheetah Aug 2 '15 at 7:39

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