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What is the sum of all the possible values of a for which 25x^2+(a−15)x+9 has exactly one distinct real root?

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    To have one real root, the discriminant must be zero

    (a-15)^ - 4(25)(9) = 0
    (a-14)^2 = 900
    a-15 = ± 30
    a = 15 ± 30
    a = 45 or a = -15

    so the sum of the a's = 45-15 = 30

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