What is the sum of all numbers a for which the graph of y=x^2+a and the graph of y=ax intersect one time?

y = x^2 + a

y = ax

Set these equal

x^2 + a = ax

x^2 - ax + a = 0

If they intersect once.....then there is only one root which means that the discriminant = 0

a^2 - 4a = 0 factor

a( a - 4) = 0

a = 0 or

a = 4

So....the sum is 4