Show that a quadratic function is always positive for all real values of $x$

Question

How can I show that $x^2 +x +1$ is aways positive for all values of $x$? Do I use discriminant or completing the square?

Answer 1

$x^2+x+1$

$=(x^2+2x+1)-x$

$=(x+1)^2-x$

Now,$(x+1)$ $>$ $x$.

So,$(x+1)^2$ $>$ $x$

So,$(x+1)^2$ $-$ $x$ is positive.