A discriminant calculator is an online tool that provides the discriminant value for given coefficients in a quadratic equation. STUDYQUERIES’s online discriminant calculator tool makes the calculations faster and easier, displaying the value in a fraction of a second.

How to Use the Discriminant Calculator?

To use the discriminant calculator, follow these steps:

  • Step 1: Enter coefficient values such as “a”, “b”, and “c” in the fields provided
  • Step 2: Now click on “Calculate” to see the result
  • Step 3: The discriminant value is displayed in the output field

Discriminant Calculator

What Is Discriminant?

The quadratic formula is $$x= \frac{-b \pm \sqrt {b^2-4ac}}{2a}$$

It can be found by using the quadratic formula to find a discriminant function. It is represented as b²-4ac and the discriminant can be zero, positive, or negative. This indicates whether there will be no solution, one solution, or two solutions.

Discriminant Calculator
Discriminant Calculator

Observe the following characteristics of discriminant algebra’s formula:

  • A zero discriminant indicates that there are repeated real number solutions to the quadratic;
  • In the case of a negative discriminant, neither of the solutions are real;
  • The quadratic equation has two distinct solutions that are real numbers for a positive discriminant.

The following quadratic equation illustrates to the students how to determine the discriminant by showing a variety of solutions.

For example, the given quadratic equation is $$6x^2 + 10x – 1 = 0$$

From the above equation, it can be seen that:

a = 6, b = 10, c = -1

When the numbers are applied to discriminant analysis – $$b^2 − 4ac$$

$$= (10)^2 – 4 (6) (-1)$$

$$= 100 + 24$$

$$= 124$$

The discriminant being a positive number, there are two solutions to the quadratic equation.

Relationship Between Roots and Discriminant

The quadratic formula not only generates quadratic equation solutions but also tells us about the nature of the solutions. When we consider the discriminant, or the expression under the radical, $$b^2-4ac$$, it tells us if the solutions are real numbers or complex numbers and how many of each type we can expect.

Let us explore how the discriminant affects the evaluation of $$\sqrt {b^2-4ac}$$ in the quadratic formula and how it helps to determine the solution set.

If $$b^2-4ac >0$$


a, b, c = real numbers

a ≠ 0

discriminant = positive 

If the radical is positive, then the number underneath it will be positive. Since you can always find the square root of a positive number, calculating the quadratic formula will yield two real solutions (one by adding the positive square root and one by subtracting it).

If $$b^2-4ac =0$$


a, b, c = real numbers

a ≠ 0

discriminant = zero

Then you will take the square root of 0, which is 0. Since adding and subtracting 0 both give the same result, the “±” portion of the formula does not matter. There will be only one solution.

If $$b^2-4ac <0$$


a, b, c = real numbers

a ≠ 0

discriminant = negative

If the radical is negative, the value underneath it will be negative. There are no real solutions to finding the square root of a negative number because you cannot use real numbers. It is possible, however, to use imaginary numbers. Then you will have two complex solutions, one by adding the imaginary square root and one by subtracting it.

Relationship Between Roots and Discriminant
Relationship Between Roots and Discriminant

If $$b^2-4ac >0 \ as\ a\ perfect\ square\ as\ well$$


a, b, c = real numbers

a ≠ 0

discriminant = positive and perfect square 

Therefore, the roots of the quadratic equation are unequal, real, and rational.

Things to Remember While Using Quadratic Formula

  • It is absolutely crucial that the equation is arranged correctly in order to arrive at a solution.
  • Ensure that 2a and the square root of the entire (b² − 4ac) are placed at the denominator.
  • Keep an eye out for negative b². This cannot be negative, so be sure to change it to positive. The square of either positive or negative is always positive.
  • The +/- should remain. Be aware of two solutions.
  • The number will have to be rounded on a certain number of decimal places when using a calculator.


The discriminant of the quadratic formula is the quantity under the radical, $$b^2 − 4ac$$ It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0, there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions). The discriminant can also tell us about the behavior of the graph of a quadratic function.


When the Discriminant is Zero, How Many Numbers of Solution Would a Quadratic Equation Have?

The discriminant or determinant of a quadratic equation is a component of the square root of the quadratic formula, b²-4ac. The discriminant must be equal to zero for there to be a unique solution. If the discriminant is less than zero, no solution can be found. In the event that it is greater than zero, there can be two real solutions to the equation.

What are the Various Forms of a Quadratic Equation?

The three main forms of a quadratic equation are –

  • Standard form
  • Factored form
  • Vertex form.

The standard form of a quadratic equation is represented as y = ax² + bx + c, and the discriminant of a quadratic equation, in this case, is b² − 4ac. The Factored form of quadratic equation is represented as y = (ax + c) (bx + d). The Vertex form of quadratic equation is represented as y = a (x + b)² + c.

It must be noted that a, b, and c numbers.

What is the Significance of Quadratic Equations?

Quadratic equations are used in a variety of ways in our daily lives, including calculating areas, determining the profit of a product, and calculating the speed of an object. There will be at least one squared variable within the quadratic equation and represented in the form of ax² + bx + c = 0, where x is the variable, ‘a’ ‘b’ ‘c’ are constants, and ‘a’ does not amount to zero. The discriminant quadratic function can be used to find the solution to the equation.

What does a discriminant of 0 mean?

It means you have a 0 under the square root in the quadratic formula if the discriminant is 0. 0 is the square root of zero. When this occurs, the plus and minus parts of the quadratic formula just disappear. One solution remains.

What is the discriminant of 3x²- 10x =- 2?

Here, a=3, b=-10 and c=2. Substitute the values, Therefore, the discriminant of is 76.

What is discriminant in math?

Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac; for a cubic equation x³ + ax² + bx + c = 0, the discriminant is a²b² + 18abc − 4b³ − 4a³c − 27c².