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

1 Answer
Oct 2, 2015

Answer:

#x in RR#

Explanation:

Consider the related equation #x^2+x+1=0#

Evaluating the discriminant (#Delta=b^2-4ac#)
#color(white)("XXX")Delta = -3#
and we know that if #Delta < 0# there are no Real solutions.

That is #x^2+x+1# does not touch or cross the X-axis.

We know that for some values (e.g. #x=0#)
#color(white)("XXX")x^2+x+1 > 0#
and since it doesn't touch or cross the X-axis
for all Real values of #x#
#color(white)("XXX")x^2+x+1 > 0#