shubhamsrg
  • shubhamsrg
Let p(x) be a polynomial such that when divided by (x−1) it leaves the remainder 2 and when divided by (x − 2) it leaves the remainder 1. What is the remainder when it is divided by (x − 1)(x − 2)?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
when we divide by a second degree polynomial the remainder will generally be linear.so the division statement becomes\[P(x)=(x-1)(x-2)q(x)+ax+b\]does that help?
anonymous
  • anonymous
u just need to evaluate \(a\) and \(b\) regarding given conditions for problem
amistre64
  • amistre64
using the remainder thrm P(1) = 2 ; and P(2) = 1 P(x) = -x+3 is my idea

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shubhamsrg
  • shubhamsrg
@mukushla can we write like that ? a and b do not change in both eqns ?
anonymous
  • anonymous
what do u mean by both equations?
shubhamsrg
  • shubhamsrg
using p(1) and p(2),we get 2 eqns.. well is it the ggeneralised form? how?
anonymous
  • anonymous
I think that will give remainder in terms of x
shubhamsrg
  • shubhamsrg
hmm,,remainder shouldn't be some numerical ?
anonymous
  • anonymous
when we divide by a linear polynomial the remainder will be a number. when we divide by a second degree polynomial the remainder will be a linear poly. and ...
shubhamsrg
  • shubhamsrg
ahh i see...yep..got it..
shubhamsrg
  • shubhamsrg
so we have p(1) = 2 = a + b and p(2) = 1 = 2a + b is that right ?
anonymous
  • anonymous
yes thats right.
shubhamsrg
  • shubhamsrg
so rem is -x + 3 ! ahh..thank you sir..
anonymous
  • anonymous
np :)

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