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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 $c$.

 Jun 3, 2018

Hey lightning!


If a quadratic equation has exxactly one real root, the discriminant is equal to zero. 


In the quadratic equation: \(ax^2+bx+c\)


The discriminant is: \(b^2-4ac\).


In this specific problem, the discriminant is \(b^2-4c\), since \(a=1\).


From the information given, we can set up the systems:


\(b^2-4c=0,\\ b=c+1.\)


Solving the systems, we can substitute:


\((c+1)^2-4c=0\\ c=1\)


I hope this helped,



 Jun 3, 2018

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