Answer:
[tex]x^2+3x+3=0[/tex]
Step-by-step explanation:
Given : [tex]x=\frac{-3 \pm \sqrt{3}i}{2}[/tex]
To Find :Which equation has the solutions [tex]x=\frac{-3 \pm \sqrt{3}i}{2}[/tex]
Solution:
[tex]\frac{x-3 - \sqrt{3i}}{2} \times \frac{x-3+ \sqrt{3i}}{2}=0[/tex]
[tex]x^2-\frac{3-\sqrt{3}i}{2}x-\frac{3+\sqrt{3}i}{2}x+\frac{9-3i^2}{4}=0[/tex]
[tex]x^2-\frac{-6x}{2}+\frac{9-3(-1)}{4}=0[/tex]
[tex]x^2+3x+3=0[/tex]
So, equation has the solutions [tex]x=\frac{-3 \pm \sqrt{3}i}{2}[/tex] is [tex]x^2+3x+3=0[/tex]
