## anonymous 4 years ago 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

1. anonymous

Don't Cheat

2. anonymous

Donot wolfram it

3. anonymous

I won't :-)

4. anonymous

$\frac{m-\sqrt{n}}{r}$ must be root

5. anonymous

I got it to $(100x^4 +10x^2+1)(20x^2-2 +x)=0$

6. anonymous

Now I think we can solve it

7. anonymous

200 :P

8. anonymous

took me time to factorize :-/

9. anonymous

Yes, cinar is right I got 200 as well

10. anonymous

I love solving such questions, these are so fun. I hate school math

11. anonymous

$(ax^2+bx+c)*(dx^4+ex^3+fx^2+gx+h)=$ =$2000x^6+100x^3+x-2$

12. anonymous

Hmm factorization that's all, take some terms common and then try to take some more that's it

13. anonymous

14. anonymous

wow then, you saw it huh..

15. anonymous

Did you use hit and trial. or some standard manipulatoin

16. anonymous

cinar's way is a standard way. mine is kind of hit and trial with inuition maybe

17. anonymous

Fact about polynomials is that any polynomial can be factorised into quadratic and linear factors but it is not always feasible

18. anonymous

Solivng a system of six equation doesnot seem promising also equatoins are not all linear

19. anonymous

hmm yeah. so what do you suggest what should we use?

20. anonymous

Cinar..we would find three sets of a,b,c But how to solve the system

21. anonymous

sorry guys, I have no time now, I can see it at night..

22. anonymous

Alright Meet me tommorrow 12:00 pm IST

23. anonymous

For more such problems Ishaan

24. anonymous

IST? Indian Standard Time? you from India?

25. anonymous

ya

26. anonymous

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

27. anonymous

Cool!