Question

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

Hint: This must be a perfect square -- in the form (a + b)^2 or (a - b)^2.

Consider both the cases.

Answer 2

45

Answer 3

solutions are

a-15=30 i.e a=45

a-15=-30 i.e a=-15

therefore, answer is 30