please help

If the polynomial  has one real root, the discriminant [ b^2 - 4ac ] must  = 0

So   a  =1, b  = c+ 1 ...so we have

(c + 1)^2  - 4(1)c    simplify

c^2 + 2c + 1  - 4c  = 0

c^2 - 2c + 1  = 0      factor the left side

(c - 1)^2  = 0         take the square root of both sides

c - 1  = 0

c  = 1

Thank you, that was fast!