Answer:
Option A is correct.
Solution = [tex]x = -2 + i\sqrt{2}[/tex]
Step-by-step explanation:
A quadratic equation is of the form [tex]ax^2+bx+c=0[/tex] .....[1]
then, the solution is given by;
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] where a, b and c are the coefficients and x is the variable.
Given the equation: [tex]x^2+4x+6=0[/tex]
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;
[tex]x = \frac{-4\pm\sqrt{4^2-4(1)(6)}}{2(1)}[/tex]
or
[tex]x = \frac{-4\pm\sqrt{16-24}}{2}[/tex]
[tex]x = \frac{-4\pm\sqrt{-8}}{2}[/tex]
We know that : [tex]i^2 = -1[/tex] where i is the imaginary part.
[tex]x = \frac{-4\pm\sqrt{8i^2}}{2}[/tex]
or
[tex]x = \frac{-4\pm 2i\sqrt{2}}{2}[/tex]
Simplify:
[tex]x = -2 \pm i\sqrt{2}[/tex]
Therefore, the solution for the given equation is, [tex]x = -2 + i\sqrt{2}[/tex]
