Question

What is the discriminant of `4/3x^2 - 2x + 3/4 = 0` and what does that mean?

Answer 1

The discriminant is zero. It tells you that there are two identical 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

`4/3x^2 – 2x +3/4 = 0`

`Δ = b^2 – 4ac = (-2)^2 -4×4/3×3/4 = 4 – 4 = 0`

This tells you that there are two identical real roots.

We can see this if we solve the equation.

`4/3x^2 – 2x +3/4 = 0`

`16x^2 -24x +9 = 0`

`(4x-3)(4x-3) = 0`

`4x-3 = 0` and `4x -3 = 0`

`4x = 3` and `4x = 3`

`x = 3/4` and `x = 3/4`

There are two identical roots to the equation.