Discriminant Calculator

Evaluate the quadratic equation discriminant value with the help of a discriminant calculator for the specified coefficient.

\( a x^2 + bx + c = 0 \)

Discriminant Formula for Quadratic Equation

The discriminant formula for the quadratic equation \(ax^2 + bx + c = 0\), where \( a ≠ 0 \), is \(b^2 – 4ac \).

The discriminant is also represented by the symbol \(Δ\).

\(∴ Δ = b^2 – 4ac \)

Make your calculations simple and easy using an online discriminant calculator from mathematics master to get your results with the snap of the hand.

Graphs of \( y = ax^2 + bx + c \) Discriminant Number of types and solutions
discriminant D is smaller than 0 Discriminant is negative No x-intercepts
No Roots
Two imaginary solutions
discriminant D equals 0 Discriminant is zero One x-intercept
One Root (a double root)
One real solution
discriminant D exceeds 0 Discriminant is positive Two x-intercepts
Two Roots
Two real solutions

Define Discriminant

It is the root that leads to quadratic equations and defines the characteristics, types, and differences. The equation can differentiate between the following types of answers.

  • In the value with positive discriminant, we get two real solutions.
  • For zero discriminant value there i one real solution.
  • In the negative value, there are two complex solutions.

What does discriminant in Maths stand for?

The value used to assess the types of solutions in incorporating the quadratic formula is known as the discriminant. It is the unique feature of quadratic equations coefficient that provides information regarding roots.

The discriminant differentiates between three types different types of quadratic equation solutions.

Case 1: If the discriminant D exceeds 0, we can take the square root and get two valid answers.

Consider a=2, b=5, c=3

\( =b^2-4ac \)

\(=(5)^2-4(2)(3) \)

\(=25-24 \)

\(= 1\)

discriminant D exceeds 0

Case 2: There is only one real solution if the discriminant D equals 0, which may be found by taking the square root of 0.

Consider a=4, b=4, c=1

\( =b^2-4ac \)

\(=(4)^2-4(4)(1) \)

\(=16-16 \)

\(= 0\)

discriminant D equals 0

Case 3: If the discriminant D is smaller than 0, we can get two complex solutions by taking the square root of a negative number.

Consider a=1, b=4, c=6

\( =b^2-4ac \)

\(=(4)^2-4(1)(6) \)

\(=16-24 \)

\(= -8\)


discriminant D is smaller than 0

How to calculate discriminant with the aid of a discriminant calculator?

Follow the instructions below to use the discriminant calculators.

  1. Select the polynomial degree ranging from 2-5 that includes quadratic, quartic, cubic, and quintic polynomials. (degrees 2, 3, 4, 5).
  2. To calculate the discriminant of quadratic equations choose second degree and proceed.
  3. Put all your polynomial coefficients including the coefficient with zero values in the equation.
  4. To get the outcome click solve.
  5. The discriminant value will be available in the output field.


What do the discriminants inform us about?

They give us the type of solutions like 1,2 or no solutions.

If the significance is more than zero what number of solutions are possible?

If the square is perfect solutions are two, otherwise there are two rational roots and two irrational roots.

What is the significance of discriminant value in a quadratic equation?

The discriminant value unveils the features of quadratic equation roots. The equation can have complex and real roots and this discriminant value helps in finding the right equation solution.

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