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a polynomial in x of the third degree which will vanish when x=1 and x= -2 and will have the values 4and 28 when x= -1 and x=2 respectively is________.

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asked by kabhir
  1. If f(x) will "vanish" when x = 1 and x = -2
    (x-1) and (x+2) must be factors

    assume we have
    f(x) = a(x+b)(x-1)(x+2)

    given:

    f(-1) = 4 ---> 4 = a(-1+b)(-2)(1)
    -2a(-1+b) = 4
    2a - 2ab = 4
    a - ab = 2

    f(2) = 28 ---> 28 = a(2+b)(1)(4)
    4a(2+b) = 28
    8a + 4ab = 28
    2a + ab = 7

    add them:
    3a=9
    a=3
    if a=3 in 2a + ab = 7
    6 + 3b=7
    3b=1
    b=1/3

    f(x) = 3(x + 1/3)(x-1)x+2)

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    posted by Reiny

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