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

1 Answer

Jul 22, 2015

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 $x$

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