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

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

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##