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March 28, 2017

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if x3+ax2-bx+10 is divisible by x2-3x+2 .find the value of a and b

  • math - ,

    since x^2 - 3x + 2 = (x-2)(x-1)
    so x^3 + ax^2 -bx + 10 must be divisible by both
    x-2 and x-1

    let f(x) = x^3 + ax^2- bx + 10
    f(2) = 5 + 4a - 2b + 10 = 0 ---> 4a - 2b = -15
    f(1) = 1 + a - b + 10 ---> a-b = -11 or a = b-11

    sub 2nd into 1st
    4(b-11) - 2b = -15
    4b - 44 - 2b = -15
    2b = 29
    b = 29/2
    then a = 29/2 - 11 = 7/2

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