Question

Which equation has the solutions x = StartFraction negative 3 plus-or-minus StartRoot 3 EndRoot i Over 2 EndFraction?

Answer 1

Answer:

x² + 3x + 3 = 0

Step-by-step explanation:

The equation has the solutions $x = \frac{- 3 \pm\sqrt{3}i}{2}$.

The equation is a quadratic equation having two roots α and β, and they are  

α = $\frac{- 3 + \sqrt{3}i}{2}$ and β = $\frac{- 3 - \sqrt{3}i}{2}$

Therefore, sum of the roots (α + β) = - 3 and the product of the roots  

α×β  

= $(\frac{- 3 + \sqrt{3}i}{2})(\frac{- 3 - \sqrt{3}i}{2})$

= $\frac{(- 3)^{2} - (\sqrt{3}i)^{2}}{2^{2} }$

= $\frac{9 + 3}{4}$

= 3

Therefore, the equation is x² - (α + β)x + αβ = 0

⇒ x² + 3x + 3 = 0 (Answer)

Answer 2

Answer:

The answer is: C .

x² + 3x + 3 = 0

I hope this helps:)