Can you please explain the question descriptively?

y^2+k^2=2(k+1)y

y^2-2(k+1)y+k^2=0

Here, a = 1, b = -2(k+1), c = k^2

 

Since, roots are equal, D = 0

b^2 - 4ac = 0

4(k+1)^2 - 4k^2 = 0

(k+1)^2 - k^2 = 0

k^2 + 2k + 1 - k^2 = 0

2k+1=0

k=-1/2