Compute Discriminant to discriminate between Real and Complex Solutions

x2+x+=0

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

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

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.

What is the Discriminant in Math?

The Discriminant D= b^2-4*a*c is part of the 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 the above Example we had 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 our 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/