Answer:
A
Step-by-step explanation:
Given the quadratic function
[tex]f(x)=2x^2-4x+5[/tex]
In this function expression,
[tex]a=2\\ \\b=-4\\ \\c=5[/tex]
Find the discriminant
[tex]D=b^2-4ac=(-4)^2-4\cdot 2\cdot 5=16-40=-24[/tex]
Note that
[tex]-1=i^2,[/tex]
then
[tex]D=-24=24i^2\\ \\\sqrt{D}=\sqrt{24i^2}=2\sqrt{6}i[/tex]
Therefore,
[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-(-4)-2\sqrt{6}i}{2\cdot 2}=\dfrac{4-2\sqrt{6}i}{4}=1-\dfrac{\sqrt{6}}{2}i\\ \\x_2=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-(-4)+2\sqrt{6}i}{2\cdot 2}=\dfrac{4+2\sqrt{6}i}{4}=1+\dfrac{\sqrt{6}}{2}i[/tex]
