If the polynomial x^2+bx+c has exactly one real root and b=c+1, find the value of the product of all possible values of c.

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!