Question

Solve −3x^2 − 4x − 4 = 0.

A) x equals quantity of 2 plus or minus 4i square root of 2 all over 3
B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3
C) x equals quantity of negative 2 plus or minus 2i square root of 2 all over 3
D) x equals quantity of negative 2 plus or minus 4i square root of 2 all over 3

Answer 1

x =(4-√-32)/-6=2/-3+2i/3√ 2 = -0.6667-0.9428i
x =(4+√-32)/-6=2/-3-2i/3√ 2 = -0.6667+0.9428i

Answer 2

For this case we have the following polynomial:

`-3x^2 - 4x - 4 = 0`
We apply the formula of the resolvent to solve the problem.
We have then:

`x = (-b +/- √(b^2 - 4ac))/(2a)`
Substituting values:

`x = (-(-4) +/- √((-4)^2 - 4(-3)(-4)))/(2(-3))`
Rewriting the equation we have:

`x = (4 +/- √(16 - 48))/(-6)`

`x = (4 +/- √(-32))/(-6)`

`x = (4 +/- √(-2*16))/(-6)`

`x = (4 +/- 4i√(2))/(-6)`

`x = (-2 +/- 2i√(2))/(3)`
Answer:
The roots of the polynomial are given by:

`x = (-2 +/- 2i√(2))/(3)`
C) x equals quantity of negative 2 plus or minus 2i square root of 2 all over 3