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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)?

  • one year ago
  • one year ago

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  1. mukushla
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    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?

    • one year ago
  2. mukushla
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    u just need to evaluate \(a\) and \(b\) regarding given conditions for problem

    • one year ago
  3. amistre64
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    using the remainder thrm P(1) = 2 ; and P(2) = 1 P(x) = -x+3 is my idea

    • one year ago
  4. shubhamsrg
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    @mukushla can we write like that ? a and b do not change in both eqns ?

    • one year ago
  5. mukushla
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    what do u mean by both equations?

    • one year ago
  6. shubhamsrg
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    using p(1) and p(2),we get 2 eqns.. well is it the ggeneralised form? how?

    • one year ago
  7. sauravshakya
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    I think that will give remainder in terms of x

    • one year ago
  8. shubhamsrg
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    hmm,,remainder shouldn't be some numerical ?

    • one year ago
  9. mukushla
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    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 ...

    • one year ago
  10. shubhamsrg
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    ahh i see...yep..got it..

    • one year ago
  11. shubhamsrg
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    so we have p(1) = 2 = a + b and p(2) = 1 = 2a + b is that right ?

    • one year ago
  12. mukushla
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    yes thats right.

    • one year ago
  13. shubhamsrg
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    so rem is -x + 3 ! ahh..thank you sir..

    • one year ago
  14. mukushla
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    np :)

    • one year ago
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