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

1 Answer
Jul 16, 2015

Answer:

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.