Question

Which of the following is a solution of x2 + 4x + 6? −2 + i times the square root of 2 2 + i times the square root of 2 −2 + three i times the square root of 2 −2 + three i times the square root of 2

Answer 1

`x^(2)+4x+6=0 \\ \\ \Delta=4^(2)-4*1*6=16-24=-8 \\ \\ √(\Delta)= √(-8) =2i √(2) \\ \\ x_(1)= (-4-2i √(2) )/(2) =-2-i √(2) \\ \\ x_(2)= (-4+2i √(2) )/(2)=-2+i √(2)`

Answer 2

Option A is correct.

Solution =
`x = -2 + i√(2)`

Explanation:

A quadratic equation is of the form
`ax^2+bx+c=0` .....[1]

then, the solution is given by;

`x = (-b\pm√(b^2-4ac))/(2a)` where a, b and c are the coefficients and x is the variable.

Given the equation:
`x^2+4x+6=0`

On comparing the given equation with equation [1] we have;

a = 1 , b = 4 and c =6

then;

the solution for the given equation is;

`x = (-4\pm√(4^2-4(1)(6)))/(2(1))`

or

`x = (-4\pm√(16-24))/(2)`

`x = (-4\pm√(-8))/(2)`

We know that :
`i^2 = -1` where i is the imaginary part.

`x = (-4\pm√(8i^2))/(2)`

or

`x = (-4\pm 2i√(2))/(2)`

Simplify:

`x = -2 \pm i√(2)`

Therefore, the solution for the given equation is,
`x = -2 + i√(2)`