Question

What is the discriminant of `x^2 -11x + 28 = 0` and what does that mean?

Answer 1

The discriminant is 9. It tells you that there are two real roots to the equation.

Explanation:

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.

• 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.

Your equation is

`x^2 -11x +28 = 0`

`Δ = b^2 – 4ac = 11^2 -4×1×28 = 121 – 112 = 9`

This tells you that there are two real roots.

We can see this if we solve the equation.

`x^2 -11x +28 = 0`

`(x-7)(x-4) = 0`

`(x-7) = 0 or`(x-4) = 0#

`x=7` or `x = 4`

There are two real roots to the equation.