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Algebra

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7 Aug 2008 19:48:53 IST

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Roots of Polynomial

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Prove that if a,b,c are real numbers such that a²+c²<4b, then the polynomial x⁴+ax³+bx²+cx+1 has no real zeros.

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Dipanjan

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Joined: 30 Jul 2008

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8 Aug 2008 15:06:41 IST

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Re:Roots of Polynomial

Hari Shankar

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Joined: 28 Feb 2007

Posts: 2173

8 Aug 2008 15:12:29 IST

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That's a clever way of replacing b that had not occurred to me.

But the method is essentially using sum of squares to prove that the expression is strictly greater than zero and hence has no real roots

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