Question

For which values of c does the following polynomial have two complex roots? X^2+4x+C

Answer 1

For this case we have that by definition, the discriminant of a quadratic expression is given by:

$d = b ^ 2-4 (a) (c)$

If the discriminant is less than zero then the expression has two different complex roots.

In this case we have the following expression:

$x ^ 2 + 4x + c$

So we have to:

$a = 1\\b = 4\\c = c$

The discriminant is given by:

$d = 4 ^ 2-4 (1) (c)\\d = 16-4c$

Then, if we want two complex roots it must be fulfilled that:

$16-4c$

Thus, the expression has two complex roots for all values greater than 4.

ANswer:

$c> 4$