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

1 Answer
Jul 15, 2015

Answer:

The discriminant of #x^2+2x+8 = 0# is #(-28)# which means that this equation has no Real solutions.

Explanation:

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

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

Seen in this context, it should be clear why:
#color(white)("XXXX")##Delta { ( > 0, rarr, 2 " Real solutions"), (=0,rarr, 1 " Real solution"), (< 0, rarr, " no Real solutions"):}#

For the given quadratic
#color(white)("XXXX")##x^2+2x+8 = 0#
the discriminant is
#color(white)("XXXX")##Delta = 2^2 - 4(1)(8) = -28#
which tells us that this equation has no Real solutions.