Question

What is the sum of all the possible values of a for which 25x2+(a−15)x+9 has exactly one distinct real root?

Answer 1

Let 25x^2+(a−15)x+9=0

Discriminant B^2-4AC=0 (only one distinct root)
(a-15)^2-4(25)(9)=0
(a-15)^2=900
a=15+30 or a=15-30
a=45 a=-15
therefore sum of a =45+(-15)
a =30