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.
We have that
x^2 + (c + 1)x + c = 0
If this has one real root, it is a double-root and the discriminant = 0
So.......
(c + 1)^2 - 4(1)c = 0
c^2 + 2c + 1 - 4c = 0
c^2 - 2c + 1 = 0 factor
(c - 1)^2 = 0
So.....c = 1
This is the only value of c that makes this true....
+80 
