
#1

Now

Roots are real and equal
#2

Now

Roots are real and rational
#3

Now

Roots are real and distinct and irrational.
#4

Now

Roots are real and distinct and irrational.
#5
x^2+5x+10=0
Now

Roots are not real.
#6
x^2-3x+1=0

Roots are real and distinct and irrational