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#1 Re: This is Cool » Cauchy–Schwarz–Bunyakovsky inequality » 2010-11-16 12:56:45

Basically, the roots cannot be real. Consider the quadratic equation as a parabola. If the equation has real roots then it crosses the x axis twice and has negative values between them, but we know that our quadratic function cannot be negative, so the roots have to be imaginary and so the discriminant has to be less than zero.

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