perplexus.info :: Just Math : 3 Distinct Roots Not

3 Distinct Roots Not (Posted on 2008-03-04)

Prove that the equation

牋爔³ + 2px² + 2p²x + p = 0

cannot have three distinct real roots, for any real number p.

See The Solution Submitted by Bractals

Rating: 4.0000 (2 votes)

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Viete!

| Comment 2 of 4 |

Hi,

From Viete

x1+x2+x3=-2p

x1*x2+x2*x3+x3*x1=2*p^2

x1^2+x2^2+x3^2=(-2*p)^2-2*2*p^2=0

one (in fact two!) of the roots must be complex!

Posted by Chesca Ciprian on 2008-03-05 07:43:13

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