If the polynomial x^2 + bx + c has exactly one real root and b = c - 2, find the value of the product of all possible values of c.
+35 Since we are told that the polynomial x^2+bx+c has exactly one real root, we know that the discriminant (b^2-4ac) is equal to 0. Thus, plugging in a = 1 and b = c-2 into the equation, we get c^2 - 8c + 4 = 0. I think this will give us c = 4 +- 2sqrt(3), so the product of all possible values of c is [4+2sqrt(3)][4-2sqrt(3)] = 16 - 12 = 4.
