The quadratic x^2 + 5x + c = 0 has roots in the form of $x = \frac{-5 \pm \sqrt{17}}{2}$. What is the value of ?

x^{2}+5x+c=0 => a=1, b=5, c=? => b^{2} = 25, 4ac = 4c => b^{2} - 4ac = 17 => 25 - 4c = 17 => c = 2.

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)