Question

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

Answer 1

Option 1)
`x=-2+i√(2)`

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√(-8)} {2}`

Remember that

`i=√(-1)`

so

`x=\frac{-4\pm i√(8)} {2}`

`x=\frac{-4\pm2i√(2)} {2}`

`x=-2\pm i√(2)`

The solutions are

`x=-2+i√(2)`

and

`x=-2-i√(2)`