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

1 Answer
Jul 22, 2015

Answer:

The discriminant of #x^2-2=0# is 8,
which means there are 2 Real solutions to this equation.

Explanation:

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

#Delta {(< 0, rarr "there are no Real solutions"), (= 0, rarr "there is exactly 1 Real solution"), (> 0, rarr "there are 2 Real solutions") :}#

Converting the given equation #x^2 -2 = 0#
into standard form
#color(white)("XXXX")##1x^2 +0x -2 = 0#
gives us
#color(white)("XXXX")##a=1##color(white)("XXXX")##b=0##color(white)("XXXX")##c=-2#

So the discriminant is
#color(white)("XXXX")##Delta = 0^2 - 4(1)(-2) = +8#

which implies that there are 2 Real solutions for #x#