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burhan101

When [equation] is divided by (x-1) the remainder is 7. When it is divided by (x+1) the remainder is 3. Determine the values of a &b . Can somebody please just explain the method... thanks:)

  • one year ago
  • one year ago

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  1. burhan101
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    \[\huge x^4-4x^3+ax^2+bx+1 \]

    • one year ago
  2. wio
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    Have you tried synthetic division?

    • one year ago
  3. burhan101
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    but there are 3 variables .. :S

    • one year ago
  4. wio
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    Yeah but you know a lot of algebra to deal with them.

    • one year ago
  5. wio
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    Hmmm, I'm not exactly sure what the trick for this is.

    • one year ago
  6. wio
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    \[ \large x^4-4x^3+ax^2+bx+1=(x-1)(cx^3+dx^2+ex+f)+7 \]

    • one year ago
  7. matricked
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    @ burhan101 use factor and remainder theorem

    • one year ago
  8. matricked
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    when f(x) is divided by (x-a) the remainder is given by f(a)

    • one year ago
  9. matricked
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    thus here f(x) =x^4−4x^3+ax^2+bx+1 f(1)=7 and f(-1)=3 u will get two equation in two unknowns and u can solev them to know a and b

    • one year ago
  10. matricked
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    thus a+b=9 and a-b -3 thus solving above two eq we have a=3 and b=6

    • one year ago
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