Answer: Option A
[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function.
For a function of the form
[tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case the function is:
[tex]2x^2-6x+5=0[/tex]
So
[tex]a=2\\b=-6\\c=5[/tex]
Then using the quadratic formula we have that:
[tex]x=\frac{-(-6)\±\sqrt{(-6)^2-4(2)(5)}}{2(2)}[/tex]
[tex]x=\frac{6\±\sqrt{36-40}}{4}[/tex]
[tex]x=\frac{6\±\sqrt{-4}}{4}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{6\±\sqrt{4}*\sqrt{-1}}{4}[/tex]
[tex]x=\frac{6\±\sqrt{4}i}{4}[/tex]
[tex]x=\frac{6\±2i}{4}[/tex]
[tex]x=\frac{3\±i}{2}[/tex]
[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]
