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 ?
+240 The quadratic formula is in format,
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
In this equation, \(x^2 + 5x + c = 0\), a = 1, and b = 5, as we are given that. The only term in the formula that contains c is the discriminant, \(\sqrt{b^2-4ac} = \sqrt{17}\)
Square both sides,
\(b^2-4ac = 17\)
Plug in known values,
\(25-4c = 17\)
Subtract 25 on both sides and divide by -4 to get c = 2
