Answer:
Option c is correct.
Step-by-step explanation:
We have been given the solution of the equation:
[tex]x=\frac{-3\pm\sqrt{3i}}{2}[/tex]
We will use the formula for finding the solutions of quadratic equation.
[tex]D=b^2-4ac[/tex]
Then [tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
Equation [tex]x^2+3x+3=0[/tex]
a=1,b=3 and c=3
[tex]D=3^3-4(1)(3)[/tex]
[tex]D=9-12=-3[/tex]
Now,[tex]x=\frac{-3\pm\sqrt{-3}}{2}[/tex]
And [tex]\sqrt{-1}=i[/tex]
So, [tex]x=\frac{-3\pm\sqrt{3i}}{2}[/tex]
Therefore Option c is correct.
