Question

show that x^2+x+1=0 has no real roots

Answer 1

we have equation...

x^2+x+1=0

or x^2 +2(x)(1/2) +1/4 - 1/4 +1=0

or (x+1/2)^2 -1/4 +4/4=0

or (x+1/2)^2+3/4=0
=> (x+1/2)^2=-3/4
=> x=+-√(-3/4) -1/2
It shows that x is not real.