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

Jul 16, 2015

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

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

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.

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

$16 {x}^{2} - 24 x + 9 = 0$

$\left(4 x - 3\right) \left(4 x - 3\right) = 0$

$4 x - 3 = 0$ and $4 x - 3 = 0$

$4 x = 3$ and $4 x = 3$

$x = \frac{3}{4}$ and $x = \frac{3}{4}$

There are two identical roots to the equation.