Given that the following equation $$p(x)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n=0$$ has $n$ distinct real roots. Prove that $$\frac{n-1}{n}>\frac{2a_0a_2}{a_1^2}$$
Prove that $\frac{n-1}{n}>\frac{2a_0a_2}{a_1^2}$
5
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calculus
polynomials
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0You need to add that $n$ distinct real roots. (For $n=2$, this gives the condition $a_1^2 > 4a_0 a_2$) – 2012-10-21
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0Yes, real roots, sorry – 2012-10-21
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0Woah, neat. I would have thought you could find $a_i$ that break this condition, but they all give polynomials with nondistinct or nonreal roots! – 2012-10-21