Question

Which of the following is a solution of x^2+4x+6

Answer 1

Answer:

Option 1) $x=-2+i\sqrt{2}$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +4x+6=0$  

so

$a=1\\b=4\\c=6$                

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(1)(6)}} {2(1)}$

$x=\frac{-4\pm\sqrt{-8}} {2}$

Remember that

$i=\sqrt{-1}$

so

$x=\frac{-4\pm i\sqrt{8}} {2}$

$x=\frac{-4\pm2i\sqrt{2}} {2}$

$x=-2\pm i\sqrt{2}$

The solutions are

$x=-2+i\sqrt{2}$

and

$x=-2-i\sqrt{2}$