Question

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

Answer 1

The answer is: C .

x² + 3x + 3 = 0

I hope this helps:)

Answer 2

x² + 3x + 3 = 0

Explanation:

The equation has the solutions
`x = (- 3 \pm√(3)i)/(2)`.

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

α =
`(- 3 + √(3)i)/(2)` and β =
`(- 3 - √(3)i)/(2)`

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

α×β

=
`((- 3 + √(3)i)/(2))((- 3 - √(3)i)/(2))`

=
`((- 3)^(2) - (√(3)i)^(2))/(2^(2) )`

=
`(9 + 3)/(4)`

= 3

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

⇒ x² + 3x + 3 = 0 (Answer)