Loser66
  • Loser66
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) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
@zzr0ck3r Please.
Loser66
  • Loser66
@dan815 @ikram002p
anonymous
  • anonymous
yes please

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More answers

ikram002p
  • ikram002p
for tomorrow xD
Loser66
  • Loser66
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. :(
ikram002p
  • ikram002p
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
Loser66
  • Loser66
hey, go to bed, my friend. It is not that. K(x) =ax +b, it is a first degree polynomial.
ikram002p
  • ikram002p
i should do that lol
Loser66
  • Loser66
hehehe.. I am using group theory to solve it or remainder theorem, but it sounds awkward hehehe... not know how to solve it yet.
Loser66
  • Loser66
\(P(x) = a_nx^n+a_{n-1}x^{n-1}+...............+a_0\) what??? I saw @electrokid really???
anonymous
  • anonymous
yo
Loser66
  • Loser66
hey, is it you?? @electrokid or the net is crazy??
Loser66
  • Loser66
wwwwwwoaaaaaaah, how are you?? @Francesco1907 Sorry friend, I am so excited now, can't think anything.
anonymous
  • anonymous
ok still waiting for the answer
anonymous
  • anonymous
isnt this the remainder theorem? If remainder of division by polynomial \(P(x)\) by \((x-a)\) is \(b\), then, \(P(a)=b\).
Loser66
  • Loser66
Yes, it is.
Loser66
  • Loser66
P(2) =3 P(-1) =-2 so??
anonymous
  • anonymous
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)
anonymous
  • anonymous
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
Loser66
  • Loser66
@electrokid I don't think so. \(P(x) = M(x) (x+2)(x-1) + K(x) \)
Loser66
  • Loser66
@adxpoi I think you are right.
Loser66
  • Loser66
but the equations are 2a+b =3 -a+b = -2
anonymous
  • anonymous
Yup, @adxpoi got it :)
Loser66
  • Loser66
@Francesco1907 take it, please. You have to do the rest.
anonymous
  • anonymous
Can I ask 1 more question
anonymous
  • anonymous
Please
anonymous
  • anonymous
Yeah sorry my bad, replace x by a in my last post :P
Loser66
  • Loser66
@Francesco1907 post a new one by yourself.
anonymous
  • anonymous
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Loser66
  • Loser66
hey, it is 0, I think and it is not hard to see it, right? just take derivative and plug pi/10 in.
anonymous
  • anonymous
nope we found it its -5 mate
Loser66
  • Loser66
how? show me. Don't forget chain rule
anonymous
  • anonymous
solve me 57 while I am solving your question
1 Attachment
Loser66
  • Loser66
I got -1/5
anonymous
  • anonymous
thats not the correct answer mate
amilapsn
  • amilapsn
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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