Check the Polynomial belongs to unit open disk?

I have problem about the polynomial. Given the polynomial, $p(x)$ , where $p(x) = p_{k} x^{n} + p_{(k-1)} x^{n-1} + ...... + p_{0} x^{0}$ . How to check, whether all root belong to open unit disk $|z| < 1$ ? By reading the references, I have founded the Lehmer's method can be used to solve this problem. But, until right now, I don't understand.. I implement it too into computer programming as the programming excersice.. Any help, thank you very much :)

#HelpMe! #MathProblem

Easy Math Editor

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Comments

Not answering your question, but $k=n$ , right? So why don't you use just one variable? :)

Tim Vermeulen - 7 years, 10 months ago

I am sorry, you're right. I have edited, that $p_{k}$ and next are the coeficient of the polynomial. Means, the general polynomial to declare. Yes, it is using one variable that $x$ .

Andrias Meisyal - 7 years, 10 months ago

Anyone?

Andrias Meisyal - 7 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$