math

the roots of 2x^2 - 3x = 4 are a and b. find the simplest quadratic equation which has roots 1/a and 1/b

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  1. the sum of the roots of the original is 3/2
    the product of the roots is -2

    so a+b = 3/2
    ab = -2

    sum of new roots = 1/a + 1/b = (a+b)/(ab)
    = (3/2) / -2 = -3/4

    product of new roots - (1/a)(1/b) = 1/(ab) = -1/2

    so the new equation is
    x^2 + (3/4)x - 1/2 = 0 or
    4x^2 + 3x - 2 = 0

    based on the theorem that for
    ax^2 + bx + c = 0

    the sum of the roots is -b/a and
    the product of the roots is c/a

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