Question

11. Solve for x: x3 + 3x2 + 3x + 2 = 0

Answer 1

x = -2, (-1 + √3 i ) / 2 , (-1 - √3 i) / 2.

Explanation:

x^3 + 3x^2 + 3x + 2 = 0

f(-2) = -8 + 3*4 - 6 + 2

= -8 + 12 - 6 + 2

= 0

So (x + 2) is a factor . Dividing:

x^2 + x + 1

---------------------------------

x + 2) x^3 + 3x^2 + 3x + 2

x^3 + 2x^2

----------------

x^2 + 3x

x^2 + 2x

-----------

x + 2

x + 2.

----------

Solving x^2 + x + 1:

x = [ - 1 +/- sqrt(1 - 4*1*1) ] / 2

= (-1 + √3 i ) / 2 , (-1 - √3 i) / 2.