One of the roots of equation 2000x^6 +100x^5 +10x^3 +x -2 =0 is of form \[\frac{m+\sqrt{n}}{r}\] where m is non zero integer n and r are relatively prime natural nos.FInd value of m+n+r

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One of the roots of equation 2000x^6 +100x^5 +10x^3 +x -2 =0 is of form \[\frac{m+\sqrt{n}}{r}\] where m is non zero integer n and r are relatively prime natural nos.FInd value of m+n+r

Mathematics
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Don't Cheat
Donot wolfram it
I won't :-)

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\[\frac{m-\sqrt{n}}{r}\] must be root
I got it to \[(100x^4 +10x^2+1)(20x^2-2 +x)=0\]
Now I think we can solve it
200 :P
took me time to factorize :-/
Yes, cinar is right I got 200 as well
I love solving such questions, these are so fun. I hate school math
\[(ax^2+bx+c)*(dx^4+ex^3+fx^2+gx+h)=\] =\[2000x^6+100x^3+x-2\]
Hmm factorization that's all, take some terms common and then try to take some more that's it
I like your way though
wow then, you saw it huh..
Did you use hit and trial. or some standard manipulatoin
cinar's way is a standard way. mine is kind of hit and trial with inuition maybe
Fact about polynomials is that any polynomial can be factorised into quadratic and linear factors but it is not always feasible
Solivng a system of six equation doesnot seem promising also equatoins are not all linear
hmm yeah. so what do you suggest what should we use?
Cinar..we would find three sets of a,b,c But how to solve the system
sorry guys, I have no time now, I can see it at night..
Alright Meet me tommorrow 12:00 pm IST
For more such problems Ishaan
IST? Indian Standard Time? you from India?
ya
Yeah I like these but it's late here and I have a problem to finish. I have posted it on OpenStudy you can check it out http://openstudy.com/users/ishaan94#/updates/4f2d8011e4b0571e9cba7c3b
Cool!

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