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Loser66

  • one year ago

The remainders when a polynomial P(x) is divided by x-2 and x+1 are respectively 3 and -2. The remainder when P(x) is divided by (x^2-x-2)is K(x). What is the value of K(-4) ?

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  1. Loser66
    • one year ago
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    @zzr0ck3r Please.

  2. Loser66
    • one year ago
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    @dan815 @ikram002p

  3. anonymous
    • one year ago
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    yes please

  4. ikram002p
    • one year ago
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    for tomorrow xD

  5. Loser66
    • one year ago
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    It's ok, friend. It is not my problem, it is from other asker, I just help him to post it here because I don't know how to solve. :(

  6. ikram002p
    • one year ago
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    Hint:- (x-2) (x+1)=x^2-x-2 so The remainder when P(x) is divided by (x^2-x-2)is K(x) ={The remainders when P(x) is divided by x-2) *{The remainders when P(x) is divided by x+1) k(X)=3*-2

  7. Loser66
    • one year ago
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    hey, go to bed, my friend. It is not that. K(x) =ax +b, it is a first degree polynomial.

  8. ikram002p
    • one year ago
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    i should do that lol

  9. Loser66
    • one year ago
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    hehehe.. I am using group theory to solve it or remainder theorem, but it sounds awkward hehehe... not know how to solve it yet.

  10. Loser66
    • one year ago
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    \(P(x) = a_nx^n+a_{n-1}x^{n-1}+...............+a_0\) what??? I saw @electrokid really???

  11. anonymous
    • one year ago
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    yo

  12. Loser66
    • one year ago
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    hey, is it you?? @electrokid or the net is crazy??

  13. Loser66
    • one year ago
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    wwwwwwoaaaaaaah, how are you?? @Francesco1907 Sorry friend, I am so excited now, can't think anything.

  14. anonymous
    • one year ago
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    ok still waiting for the answer

  15. anonymous
    • one year ago
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    isnt this the remainder theorem? If remainder of division by polynomial \(P(x)\) by \((x-a)\) is \(b\), then, \(P(a)=b\).

  16. Loser66
    • one year ago
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    Yes, it is.

  17. Loser66
    • one year ago
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    P(2) =3 P(-1) =-2 so??

  18. anonymous
    • one year ago
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    P(x) = (x^2 - x- 2)Q(x) + K(x) P(2) = K(2) =3 P(-1) = K(-1) = -2 K(x) = ax + b So, 2x + b = 3 -1x + b = -2 solve these to get K(x)

  19. anonymous
    • one year ago
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    so, we follow that \[P(2)=3\] and \[P(-1)=-2\] \[P(x)=(x-2)(x+1)K(x)\] so, \[K(x)=(3)(-2)\] i.e., indepemdemt of x

  20. Loser66
    • one year ago
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    @electrokid I don't think so. \(P(x) = M(x) (x+2)(x-1) + K(x) \)

  21. Loser66
    • one year ago
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    @adxpoi I think you are right.

  22. Loser66
    • one year ago
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    but the equations are 2a+b =3 -a+b = -2

  23. anonymous
    • one year ago
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    Yup, @adxpoi got it :)

  24. Loser66
    • one year ago
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    @Francesco1907 take it, please. You have to do the rest.

  25. anonymous
    • one year ago
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    Can I ask 1 more question

  26. anonymous
    • one year ago
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    Please

  27. anonymous
    • one year ago
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    Yeah sorry my bad, replace x by a in my last post :P

  28. Loser66
    • one year ago
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    @Francesco1907 post a new one by yourself.

  29. anonymous
    • one year ago
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  30. Loser66
    • one year ago
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    hey, it is 0, I think and it is not hard to see it, right? just take derivative and plug pi/10 in.

  31. anonymous
    • one year ago
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    nope we found it its -5 mate

  32. Loser66
    • one year ago
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    how? show me. Don't forget chain rule

  33. anonymous
    • one year ago
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    solve me 57 while I am solving your question

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  34. Loser66
    • one year ago
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    I got -1/5

  35. anonymous
    • one year ago
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    thats not the correct answer mate

  36. amilapsn
    • one year ago
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    For the earlier question K(4) can be found using this method too.. (Using similar method you can find K(-4)) |dw:1440136503090:dw|

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