I can't firgure out how to show that this prove or disprove problem is false:

Prove or disprove that there exists a real number x such that x^2 + x + 1 ≤ 0.

As i said i know the problem is false for every number. I just don't know how to show it. I thought maybe by cases with x ≤ 0 and x ≥ 0.