Question

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

Answer 1

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.