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?

Answer 1

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