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

1 Answer
Jul 18, 2015

Answer:

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!