# When is the discriminant of a quadratic function imaginary?

##### 1 Answer

Oct 28, 2015

The discriminant of a quadratic function can only be imaginary if at least some of the coefficients of the quadratic are imaginary.

#### Explanation:

For a quadratic in the general form

The discriminant is

If the discriminant is negative (which might be what you intended to ask)

the square root of the discriminant is imaginary

and therefore the quadratic formula

gives imaginary values as roots for

This happens when the parabola does not touch or cross the X-axis.