What is the discriminant of 2x^2− x + 8 = 0 and what does that mean?

1 Answer
Alan P.
Jul 16, 2015

The discriminant of 2x^2-x+8 =0 is (-1)^2-4(2)(8) = -63
This tells that there are no Real roots to the given equation.

Explanation:

For a quadratic equation in the general form:
color(white)("XXXX")ax^2+bx=c = 0
the discriminant is:
color(white)("XXXX")b^2 - 4ac

The discriminant is a component of the general quadratic formula for solving a quadratic equation:
color(white)("XXXX")x = (-b+-sqrt(b^2-4ac))/(2a)

If the discriminant (b^2-4ac) is less than zero
then the "solution" requires
color(white)("XXXX")the square root of a negative value
color(white)("XXXX")color(white)("XXXX")which does not exist as any Real value,
color(white)("XXXX")color(white)("XXXX") and therefore there can be no Real solutions to the equation.

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