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burhan101

  • 2 years ago

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:)

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

  2. wio
    • 2 years ago
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    Have you tried synthetic division?

  3. burhan101
    • 2 years ago
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    but there are 3 variables .. :S

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

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

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

  7. matricked
    • 2 years ago
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    @ burhan101 use factor and remainder theorem

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

  9. matricked
    • 2 years ago
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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

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

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