[tex]\sf x^{2} + 9x + 20 = 0\\\sf a = 1 ; b = 9 ; c = 20\\\sf b^{2} -4ac - 9^{2} -4(1)(20)=81 -80=1[/tex]
Discriminant 1 is not a perfect square
Discriminant: [tex]\bold b^{2} - \bold 4 \bold a \bold c \bold > \bold 0[/tex]
Nature of discriminant: The roots are real,distinct and rational
[tex]\sf 2x^{2} -10x +8=0\\\sf a=2; b=-10; c=8\\\sf b^{2} -4ac =(-10)^{2} -4(2)(8) = 100 - 64 = 36[/tex]
Discriminant 36 is a perfect square
Discriminant: [tex]\sf b^{2} - 4ac > 0[/tex]
Nature of discriminant: The roots are real, distinct and rational
