Polynomials: Schur-Cohn Criterion. (1 Viewer)

RealiseNothing

what is that?It is Cowpea
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I think I got an answer to the first one, will post up after I finish this game of LoL.
 

RealiseNothing

what is that?It is Cowpea
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First one:

Since it's an if and only if, we have to prove it holds both ways, this is the proof for the first way:

We know

Hence we can say:



Since each bracket individually is negative and will therefore become positive. Expanding gives:



Re-arranging:



Since

We can let them equal 'c' and 'b' respectively, which by substitution gives:



Now if both are less than 1, it follows that their sum is less than 2, and their product is less than 1, hence:



As required.
 

Fus Ro Dah

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I don't think that's entirely correct as it is because you assumed there that alpha and beta are real in order to have obtained your inequality (a-1)(b-1)>0.
 

Fus Ro Dah

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That seems right but I don't really see how that constitutes a proof satisfying the 'iff' condition.
 

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