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

Jul 16, 2015

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

Explanation:

If you have a quadratic equation of the form

$a {x}^{2} + b x + c = 0$

The solution is

x = (-b±sqrt(b^2-4ac))/(2a)

The discriminant Δ is ${b}^{2} - 4 a c$.

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

• If Δ > 0, there are two separate real roots.
• If Δ = 0, there are two identical real roots.
• If Δ <0, there are no real roots, but there are two complex roots.

${x}^{2} - 2 = 0$

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#

$x = \sqrt{2}$ and $x = - \sqrt{2}$

There are two separate real roots to the equation.