Maths

Solve the equation 12xcube-8xsquare+kx+18=0 and find the value of k given that one root is negative of other

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  1. 12x^3-8x^2+kx+18 = 0
    If one root is a and the other is -a, then we have (with the third root being p)
    12(x-a)(x+a)(x-p) = 12(x^2-a^2)(x-p)
    = 12x^3-12px^2-12a^2x+12a^2p

    So, we need
    -12p = -8
    p = 2/3

    12a^2p = 18
    a^2 = 9/4
    a = 3/2

    k = -12a^2 = -27

    check: (3x-2)(2x-3)(2x+3) = 12x^3-8x^2-27x+18

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