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

1 Answer
Jun 12, 2017

Answer:

#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]}