Question

When is the discriminant of a quadratic function imaginary?

Answer 1

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
`color(white)("XXX")y=ax^2+bx+c`

The discriminant is
`color(white)("XXX")b^2-4ac`

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
`color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)`
gives imaginary values as roots for `y=0`
This happens when the parabola does not touch or cross the X-axis.