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