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:
 $x = \frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$
 Substituting values:
 $x = \frac{-(-4) +/- \sqrt{(-4)^2 - 4(-3)(-4)}}{2(-3)}$
 Rewriting the equation we have:
 $x = \frac{4 +/- \sqrt{16 - 48}}{-6}$
 $x = \frac{4 +/- \sqrt{-32}}{-6}$
 $x = \frac{4 +/- \sqrt{-2*16}}{-6}$
 $x = \frac{4 +/- 4i\sqrt{2}}{-6}$
 $x = \frac{-2 +/- 2i\sqrt{2}}{3}$
 Answer:
 The roots of the polynomial are given by:
 $x = \frac{-2 +/- 2i\sqrt{2}}{3}$
 C) x equals quantity of negative 2 plus or minus 2i square root of 2 all over 3