Question

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

Answer 1

`x in(-oo,+oo)`

Explanation:

`"check the "color(blue)"discriminant "`

`x^2+x+1" is in standard form"`

`"with " a=1,b=1" and " c=1`

`rArrb^2-4ac=1-4=-3<0`

`"hence " x^2+x+1" has no real roots"`

`"this indicates that the graph is completely above the x-axis"`

`rArrx^2+x+1>0 " for all real values of x"`

`"in interval notation " x in(-oo,+oo)`
graph{x^2+x+1 [-10, 10, -5, 5]}