Answer:
D
Step-by-step explanation:
The quadratic formula:
[tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
where a is the coefficient of [tex]x^2[/tex], b being the coefficient of [tex]x[/tex] and c being the constant.
Plug in the values:
[tex]\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}[/tex]
[tex]\frac{5\pm\sqrt{-15} }{4}[/tex]
Since [tex]\sqrt{-15} =\sqrt{-1} \sqrt{15} =i \sqrt{15}[/tex]
The answer is:
[tex]\frac{5\pm i \sqrt{15} }{4}[/tex]
