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
2x² -12x+16 has the discriminant:
= b² – 4*a*c
= (-12)² – 4*2*16
= 144 – 128 = 16
Since 16>0 2x² -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= b²-4*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 2x²+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 2x²+5x-3?
The coefficients are a=2, b=5 and c=-3.
We plug those into the formula for Discriminant D= b²-4*a*c
to get D=5²-4*2*(-3)
which simplifies to
25 – 8*(-3) = 25 + 24 = 49
implying the Discriminant is D=49.

Using the above Discriminant Calculator to solve 2x²+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.