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#### wishmaster

##### Active member

- Oct 11, 2013

- 211

I know how to find the roots with Horners method,i am just wondering if there is an easier and quicker way to find them? Thank you!

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- #1

- Oct 11, 2013

- 211

I know how to find the roots with Horners method,i am just wondering if there is an easier and quicker way to find them? Thank you!

- Mar 22, 2013

- 573

You don't have to go that far. Try proving that this factors over integers completely by applying rational root theorem (integral root theorem for monic polynomials).wishmaster said:I know how to find the roots with Horners method

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- #3

- Oct 11, 2013

- 211

I dont know how to do it......You don't have to go that far. Try proving that this factors over integers completely by applying rational root theorem (integral root theorem for monic polynomials).

- Feb 13, 2012

- 1,704

The polynomial has degree 3, so that it exists at least one real root that can be found with the Newton-Raphson method...

I know how to find the roots with Horners method,i am just wondering if there is an easier and quicker way to find them? Thank you!

- Mar 22, 2013

- 573

Rational root theorem - Wikipedia, the free encyclopediawishmaster said:I dont know how to do it......

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- Oct 11, 2013

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- Jan 17, 2013

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\(\displaystyle P(3) = 3^3-8(9)+19\times 3-12 = 27-72+57-12=0 \)

Hence \(\displaystyle x=3\) is a solution . The next step divide the cubic by \(\displaystyle (x-3)\) to get a polynomial of degree $2$.

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- #8

- Oct 11, 2013

- 211

Seems thats not the easier and faster method as Horners...or i cant see it!

- Feb 13, 2012

- 1,704

... not only neither easier nor faster... if the polynomial doesn't have rational roots [... the most probable case...] it fails!...Seems thats not the easier and faster method as Horners...or i cant see it!

Kind regards

$\chi$ $\sigma$

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- #10

- Oct 11, 2013

- 211

My question was about rational roots.....how to find them fast.... not only neither easier nor faster... if the polynomial doesn't have rational roots [... the most probable case...] it fails!...

Kind regards

$\chi$ $\sigma$

- Mar 22, 2013

- 573

Horner's method has computational complexity $\mathcal{O}(n)$, whereas RRT exceeds that quite less often, as far as I can tell.chisigma said:neither easier nor faster

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- #12

- Oct 11, 2013

- 211

So i think the answer is: Deal with it as you can?Horner's method has computational complexity $\mathcal{O}(n)$, whereas RRT exceeds that quite less often, as far as I can tell.

- Mar 22, 2013

- 573