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 <0\\16 <4c\\\frac {16} {4} <c\\4 <c`

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

ANswer:

`c> 4`