Question

How do you solve the inequality `x^2+x+1>=0` and write your answer in interval notation?

Answer 1

The solution is `x in ]-oo, +oo[`

Explanation:

Let

`f(x)=x^2+x+1`

We complete the square,

`f(x)=x^2+x+1/4+3/4`

`f(x)=(x+1/2)^2+3/4`

`AA x in RR, f(x)>0`