Respuesta :

C) Quick way:

3x^2+6x+6=0 ---> x^2+2x+2=0,

sum of solutions is the 'x' coefficient multiplied by -1:  (-1+i)+(-1-i)=-2-->2
Product is the independent term: (-1+i)(=1+i) = (-1)^2-i^2 = 1+1=2

Takes longer to write it down!

The required solution of the equation 3x² + 6x +6 = 0 is x = -1 ± i.

What is a complex number?

The number that constitutes real and imaginary numbers are called complex numbers. The standard form of the complex number is Z = a + bi, Where a = real number and bi = imaginary number.

3x² + 6x +6 = 0
For above equation
a = 3
b = 6
c = 6

[tex]x = \frac{-b \pm\sqrt{b^2 - 4ac} }{2a}[/tex]
Putting the value of a, b, and c in the above formula for getting the solution to the equation.

[tex]x = \frac{-6\pm\sqrt{6^2 - 4*3*6} }{6} \\x =\frac{-6\pm\sqrt{36 - 72} }{6}\\x=\frac{-6\pm\sqrt{-36} }{6}\\x=\frac{-6\pm6\sqrt{-i} }{6}\\x = -1\pm i[/tex]

Thus, the required solution of the equation 3x² + 6x +6 = 0 is x = -1 ± i.


Learn more about complex numbers here:
https://brainly.com/question/28007020

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