Question

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

Answer 1

$ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}\ and\ x_2=\dfrac{-b+\sqrt{\Delta}}{2a}\\\\\Delta=b^2-4ac$

$y=x^2+5x+c\\\\a=1;\ b=5;\ c=c\\\\x=\dfrac{-5\pm\sqrt\Delta}{2\cdot1}\\\\\Delta=5^2-4\cdot1\cdot c=25-4c\\\\Therefore:x=\dfrac{-5\pm\sqrt{25-4c}}{2}$