Theory of Equation (Descarte's Rule of Sign)

Most of the people I see gets confused about this rule. This rule actually cannot determine the number of roots. Specifically, this rule determines the NUMBER OF MAXIMUM real positive or negative roots by checking the number of change of signs in f(x) and f(-x). The word MAXIMUM should be given emphasis.

For the people who don't know this rule: Check this link http://en.wikipedia.org/wiki/Descartes'ruleof_signs

#Algebra #Polynomials #Root(Equation) #Theoryofequation #Descarte

Easy Math Editor

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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}`	$\boxed{123}$

Comments

Can you contribute to the wiki on Descartes Rule of Sign here on Brilliant ?

Thanks :)

A Former Brilliant Member - 6 years, 3 months ago

Sure, but can you tell me how can I contribute?

Saswata Dasgupta - 6 years, 3 months ago

It's simple really !

Just got to the link that I have provided, click on "edit this page" and add the content that you think is appropriate :)

A Former Brilliant Member - 6 years, 3 months ago

I think this rule also tells us about the complex roots.

Trishit Chandra - 6 years, 3 months ago

Obviously you can get the MAXIMUM number of complex roots by taking out the number of MAXIMUM real roots from the total roots

Saswata Dasgupta - 6 years, 3 months ago

Yes I've checked the wolfram. It also says this.

Trishit Chandra - 6 years, 2 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}`	$\boxed{123}$