+1246 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 $c$.
+985 Hey lightning!
If a quadratic equation has exxactly one real root, the discriminant is equal to zero.
In the quadratic equation: ax2+bx+c,
The discriminant is: b2−4ac.
In this specific problem, the discriminant is b2−4c, since a=1.
From the information given, we can set up the systems:
b2−4c=0,b=c+1.
Solving the systems, we can substitute:
(c+1)2−4c=0c=1
I hope this helped,
Gavin
