Given,

(k+1)x2−2(k+1)x+1=0 is a quadratic equation.

The roots of the given equation are real and equal.

Therefore, the discrimant will be equal to 0.

Discriminant, D = b2 – 4ac

[−2(k+1)]2-4(k+1)(1) = 0

4(k+1)2 = 4(k+1)

(k+1)2 = (k+1)

k2+2k+1=k+1

k2 + k = 0

k (k+1) = 0

k = 0 or k = -1

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