[tex]\\ \sf\longmapsto D=b^2-4ac[/tex]
#1
[tex]\\ \sf\longmapsto x^2+6x+9=0[/tex]
Now
[tex]\\ \sf\longmapsto D=(6)^2-4(1)(9)=36-36=0[/tex]
Roots are real and equal
#2
[tex]\\ \sf\longmapsto x^2+9x+20=0[/tex]
Now
[tex]\\ \sf\longmapsto D=(9)^2-4(1)(20)=81-80=1[/tex]
Roots are real and rational
#3
[tex]\\ \sf\longmapsto x^2+6x+3=0[/tex]
Now
[tex]\\ \sf\longmapsto D=6^2-4(1)(3)=36-12=24[/tex]
Roots are real and distinct and irrational.
#4
[tex]\\ \sf\longmapsto 2x^2-10x+8=0[/tex]
Now
[tex]\\ \sf\longmapsto D=(-10)^2-4(1)(8)=100-32=68[/tex]
Roots are real and distinct and irrational.
#5
x^2+5x+10=0
Now
[tex]\\ \sf\longmapsto D=5^2-4(1)(10)=25-40=-15[/tex]
Roots are not real.
#6
x^2-3x+1=0
[tex]\\ \sf\longmapsto D=(-3)^2-4(1)(1)=9-4=5[/tex]
Roots are real and distinct and irrational
