In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
How to determine the roots of a cubic equation
In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.
The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7
x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2
In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
To learn more on cubic equations: https://brainly.com/question/13730904
#SPJ1
