# How do you solve inequality x^2+x+1>0?

Aug 16, 2015

Solve the inequality: $f \left(x\right) = {x}^{2} + x + 1 > 0$

#### Explanation:

First, find the 2 x-intercepts (real roots) by solving
$f \left(x\right) = {x}^{2} + x + 1 = 0$.
D = d^2 = b^2 - 4ac = 1 - 4 = -3.
There is no x-intercepts. Since a > 0, the parabola opens upward and is completely above the x-axis.
The inequality f(x) > 0 is always true, regardless of x.
graph{x^2 + x + 1 [-10, 10, -5, 5]}