Answer:
x² + 3x + 3 = 0
Step-by-step explanation:
The equation has the solutions [tex]x = \frac{- 3 \pm\sqrt{3}i}{2}[/tex].
The equation is a quadratic equation having two roots α and β, and they are
α = [tex]\frac{- 3 + \sqrt{3}i}{2}[/tex] and β = [tex]\frac{- 3 - \sqrt{3}i}{2}[/tex]
Therefore, sum of the roots (α + β) = - 3 and the product of the roots
α×β
= [tex](\frac{- 3 + \sqrt{3}i}{2})(\frac{- 3 - \sqrt{3}i}{2})[/tex]
= [tex]\frac{(- 3)^{2} - (\sqrt{3}i)^{2}}{2^{2} }[/tex]
= [tex]\frac{9 + 3}{4}[/tex]
= 3
Therefore, the equation is x² - (α + β)x + αβ = 0
⇒ x² + 3x + 3 = 0 (Answer)
