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maths

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ifx^3+mx^2+nx+6 has x-2 as a factor and leaves remainder 3 when divided by x-3, find the values of m and n.

  • maths -

    let f(x) = x^3 + mx^2 + nx + 6
    given:
    f(2) = 0
    = 8 + 4m + 2n + 6 = 0 ---> 2m + n = -7
    given: f(3) = 3
    = 27 + 9m + 3n + 6 = 3 --- 3m + n = -10

    subtract the two equations to get : m = -3
    sub that into 2m+n=-7
    -6 + n = -7
    n = -1

    m= -3, n = -1

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