For this case we have that by definition, the discriminant of a quadratic equation [tex]ax ^ 2 + bx + c = 0[/tex], is given by:
[tex]d = b ^ 2-4 (a) (c)[/tex]
[tex]d> 0[/tex]: Two different real roots
[tex]d = 0[/tex]: Two equal real roots
[tex]d <0[/tex]: Two different complex roots
If we have [tex]9x ^ 2 + 12x + 4 = 0[/tex], then:
[tex]a = 9\\b = 12\\c = 4[/tex]
Substituting the values:
[tex]d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0[/tex]
Thus, we have two equal real roots.
ANswer:
We have two equal real roots.
