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4 April, 01:44

Find a quadratic equation whose roots are the reciprocals of the roots of 3x^2+5x-2=0.

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  1. 4 April, 01:47
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    3x^2 + 5x - 2 = 0

    3x^2 + 6x - x - 2 = 0

    (3x^2 + 6x) + (-x - 2) = 0

    3x (x + 2) - 1 (x + 2) = 0

    (3x - 1) (x + 2) = 0

    3x - 1 = 0 or x + 2 = 0

    3x = 1 or x = - 2

    x = 1/3 or x = - 2

    Reciprocals are 3 and - 1/2

    Equation with roots at 3 and - 1/2 is (x - 3) (x + 1/2) = x^2 - 5/2 x - 3/2 = 2x^2 - 5x - 3

    Therefore, required equation is y = 2x^2 - 5x - 3
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