### What you will learn in this mini lesson

You will learn how to find the Discriminant of a Quadratic Equations in Standard Form and its significance in solving Quadratic Equations. Our Step by Step Calculator allows you to compute the Discriminant of your own quadratic equation.**Quick Example**

2x

^{2}-12x+16 has the discriminant:

= b

^{2}– 4*a*c

= (-12)

^{2}– 4*2*16

= 144 – 128 = 16

Since 16>0 2x

^{2}-12x+16 has two real solutions. That’s all 😉

# What you need to know about the Discriminant of a Quadratic Equation

The Discriminant is the red part of the famous Quadratic Equation Formula below:

### What is the Discriminant in Math?

The Discriminant D= b^{2}-4*a*c is the part of the above Quadratic Equation. It is the part inside the square root.

The Discriminant ‘discriminates’ or ‘distinguishes’ 3 different types of solutions to the Quadratic Equation.

1) If the Discriminant D is greater than 0 then we can take the square root and we will have 2 real solutions.

2) If the Discriminant D is equal to 0 then we can take the square root of 0 and we will have 1 real solutions.

3) If the Discriminant D is less than 0 then we can take the square root of a negative number and we will have 2 complex solutions.

In below’s example we have a Discriminant D=49. Since it is a positive number we know that our Quadratic Equation 2x^{2}+5x-3=0 has 2 real (non-complex) solutions. **What you take from this is that a Discriminant tells you the type of solution of any Quadratic Equation WITHOUT given you the actual solutions. **Those solutions can be found using our handy Quadratic Equation Solver at: https://mikescalculators.com/solve-quadratic-equation/

### Example: Find the Discriminant of a Quadratic Equation

What is the Discriminant of 2x^{2}+5x-3?

The coefficients are a=2, b=5 and c=-3.

We plug those into the formula for Discriminant D= b^{2}-4*a*c

to get D=5^{2}-4*2*(-3)

which simplifies to

25 – 8*(-3) = 25 + 24 = 49

implying the Discriminant is D=49.

Using the above Discriminant Calculator to solve 2x^{2}+5x-3=0 we must enter the coefficients a=2, b=5 and c=-3.

With steps we see the Discriminant is D=49 .

Get it now? Try the above Discriminant Calculator a few more times or watch the video below.