Solve the inequality x^2+2x+6>=0.

x^2 + 2x + 6 >= 0

To
solve, we will need to find the zeros of the functions.

x1=
( -2 + sqrt(4-24) / 2 = (-2 + sqrt20*i)/2 = (-2+2sqrt5*i )
/2

==> x1= ( -2 + sqrt5*i
)

==> x2= (-2 -sqrt5*i
)

==> Then we conclude that the function has no real
zeros. The inequality is true for all real numbers .

Also,
if we draw the graph of the curve x^2 + 2x + 6 , we will notice that the curve is above
the x-axis for all values.

Then the function is always
positive and has no zeros.

==> The solution is
:

x = R ( R is a real
number)