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]
If we have the following equation:
[tex]4x ^ 2 + x + 3 = 0\\a = 4\\b = 1\\c = 3[/tex]
Then, the discriminant is given by:
[tex]d = (1) ^ 2-4 (4) (3)\\d = 1-48\\d = -47[/tex]
So we have to:
[tex]d <0[/tex], two different complex roots.
Answer:
[tex]d = -47[/tex], two different complex roots.
