Question

What is the discriminant of `8x^2+5x+6=0` and what does that mean?

Answer 1

The discriminant `Delta` can be:
`Delta>0` `=>` your equation has 2 distinct Real solutions;
`Delta=0` `=>` your equation has 2 coincident Real solutions;
`Delta<0` `=>` your equation does not have Real solutions.

Explanation:

The discriminant `Delta` is a number that characterizes the solutions of a second degree equatin and is given as:
`Delta=b^2-4ac`
Your equation is in the form `ax^2+bx+c=0` with:
`a=8`
`b=5`
`c=6`
So `Delta=25-4(8*6)=25-192=-167<0`
A negative discriminant means that your equation does not have Real solutions!