Question

Solve for x over the complex numbers.

x^2+4x+13=0

X =
or X=
(need both)
PLEASE and thank you!!

Answer 1

Explanation:

Given x^2+4x+13=0, find the complex roots. The best approach here is to use the quadratic formula. Note that a = 1, b = 4 and c = 13.

Thus, the discriminant, b^2 - 4ac, is (4)^2 - 4(1)(13) = 16 - 52 = -36, and the square root of that is plus or minus i√36, or plus or minus 6i.

plus or minus i√

Answer 2

x = - 2 + 3i or x = - 2 - 3i

Explanation:

Given quadratic equation,

`x^2 + 4x + 13=0`

By the quadratic formula,

`x=(-4\pm √(4^2 - 4* 1* 13))/(2* 1)`

`x=(-4\pm √(16-52))/(2)`'

`x=(-4\pm √(-36))/(2)`

`x=(-4\pm 6i)/(2)`

`x=-2\pm 3i`

Hence, the solution of the given equation,

x = - 2 + 3i or x = - 2 - 3i