What you will learn in this mini lessonYou 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.
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.