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Math Help - Quadratic Inequalities

  1. #1
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    Quadratic Inequalities

    Given that A and B, where A < B, are the roots of the equation 2x^2 + x -5 = 0
    Calculate the value of
    (c) A - B [Answer = -1/2 Sqrt 41]

    Sum of roots = A + B = 1/2
    Product of roots = AB = -5/2

    I have tried to use A^2 - B^2 / A + B, but I can't seem to get +B^2, since all expansions of (A-B)^2 and (A+B)^2 involve B^2

    Please help.
    Thanks
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  2. #2
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    \begin{aligned}\begin{array}{c} (a+b)^2 = a^2+2ab+b^2\\\ (a-b)^2 = a^2-2ab+b^2 \end{array} & \iff (a+b)^2-(a-b)^2 = 4ab.\end{aligned}
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