What is the discriminant of $x^2-4=0$ and what does that mean?

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Answer 1 · 2015-07-16T01:59:34

The discriminant is 8. It tells you that there are two separate real roots to the equation.

If you have a quadratic equation of the form

$ax^2+bx+c=0$

The solution is

$x = (-b±sqrt(b^2-4ac))/(2a)$

The discriminant $Δ$ is $b^2 -4ac$ .

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

Your equation is

$x^2 - 2 = 0$

$Δ = b^2 – 4ac = (0)^2 -4×1×(-2) = 0 +8 = 8$

This tells you that there are two separate real roots.

We can see this if we solve the equation.

$x^2 -2 = 0$

$x = (-b±sqrt(b^2-4ac))/(2a) = (-0±sqrt((0)^2 -4×1×(-2)))/(2×1) = ±sqrt(0+8)/2 = ±sqrt8/2 = ±(2sqrt2)/2 = ±sqrt2$ #

$x = sqrt2$ and $x = -sqrt2$

There are two separate real roots to the equation.

What is the discriminant of x^2-4=0x^2-4=0 and what does that mean?