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

Jun 12, 2017

$x \in \left(- \infty , + \infty\right)$

#### Explanation:

$\text{check the "color(blue)"discriminant }$

${x}^{2} + x + 1 \text{ is in standard form}$

$\text{with " a=1,b=1" and } c = 1$

$\Rightarrow {b}^{2} - 4 a c = 1 - 4 = - 3 < 0$

$\text{hence " x^2+x+1" has no real roots}$

$\text{this indicates that the graph is completely above the x-axis}$

$\Rightarrow {x}^{2} + x + 1 > 0 \text{ for all real values of x}$

$\text{in interval notation } x \in \left(- \infty , + \infty\right)$
graph{x^2+x+1 [-10, 10, -5, 5]}