Polynomials: Schur-Cohn Criterion. (1 Viewer)

[Fus Ro Dah]

 

[barbernator]

will try to answer this question after thursday

 

[RealiseNothing]

I think I got an answer to the first one, will post up after I finish this game of LoL.

 

[RealiseNothing]

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]

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.

 

[IamBread]

Are the coefficients real?

 

[Fus Ro Dah]

Are the coefficients real?

Yes.

 

[IamBread]

Well here's my attempt at the first one.

 

[Fus Ro Dah]

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