When is the discriminant of a quadratic function imaginary?

1 Answer
Alan P.
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
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.

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