The Discriminant Calculator is an online tool for computing the value of a polynomial equation's discriminant. This online discriminant calculator allows you to quickly determine the discriminant's value.

**Discriminant Calculator:** When solving quadratic equations, we employ the discriminant
expression b^{2} - 4ac. The discriminant formula can also be used to figure out what kind of roots an
equation has. Discriminant is a mathematical quantity derived from the coefficients of a polynomial equation
that is used further to determine the nature of the roots whether the roots of the equation are real, equal,
or imaginary.

This easy & handy online Discriminant Calculator tool makes your calculations easier and also helps you in learning the concept thoroughly. However, you can also check out the manual process to find the discriminant values with a solved example for a better understanding.

A discriminant is a function of a polynomial equations of coefficients that expresses the nature of a quadratic equation's roots. The equations may distinguish between several sorts of responses, such as:

- We find two true solutions when the discriminant value is positive.
- There is just one actual solution when the discriminant value is zero.
- We get a pair of complex solutions when the discriminant value is negative.

The standard discriminant of an equation of the form ax^{2}+bx+c = 0 is calculated using he below
given formula:

**Discriminant, D = b ^{2} – 4ac**

Where

- D is the value of the discriminant
- a is the coefficient of x
^{2} - b is the coefficient of x
- c is a constant term.

Let's go with the solved example on Discriminant Calculator and understand the concept practically in a step-wise manner.

Along with this free & handy online discriminant calculator, you can also try other math concepts calculator tools by visiting this trusted portal called arithmeticcalculator.com

**Examples on Finding Discriminant of Quadratic Equation**

1. What should be the value of discriminant (D) in the equation 2x^{2} - x + 4 ?

**Solution:**

Given that the quadratic equation is 2x^{2} - x + 4

Here, a = 2, b = -1, c = 4

The discriminant formula is D = b^{2} - 4ac

D = (-1)^{2}- 4(2)(4)

D = 1 - 32

D = - 31

Thus, the discriminant is -31 of the equation 2x^{2} - x + 4

2. What should be the value of discriminant (D) in the equation x^{2} - 3x + 2 ?

**Solution:**

Given that the quadratic equation is x^{2} - 3x + 2

Here, a = 1, b = -3, c = 2

The discriminant formula is **D = b ^{2} - 4ac **

D = (-3)^{2}- 4(1)(2)

D = 9 - 8

D = 1

Therefore, the discriminant is 1 of the equation x^{2} - 3x + 2

**1. Define discriminant?**

A discriminant is a function of a polynomial equations of coefficients that expresses the nature of a quadratic equation's roots. The equations may distinguish between several sorts of responses, such as:

- We find two true solutions when the discriminant value is positive.
- There is just one actual solution when the discriminant value is zero.
- We get a pair of complex solutions when the discriminant value is negative.

**2. Why is discriminant value important in a quadratic equation** **?**

The nature of the roots of the quadratic equation is revealed by discriminant value. Real or complex roots can be found in quadratic equations. It helps in the determination of an equation's solution.

**3. What about the standard form of discriminant ?**

The standard discriminant form for the quadratic equation ax^{2} + bx + c = 0 is

**Discriminant, D = b ^{2} – 4ac**

Where

a be the coefficient of x^{2}

b be the coefficient of x

c be a constant term.

**4. How can the discriminant value be used to determine the nature of roots?**

Different forms of roots can exist in a quadratic equation. The nature of roots is defined by the discriminant value. They are as follows:

- If D> 0, the roots are real and unequal
- If D = 0, the roots are real and equal
- If D < 0, the roots are not real (i.e., complex).

**5. In a quadratic equation, why is discriminant value important ?**

The nature of the roots of the quadratic equation is revealed by discriminant value. Real or complex roots can be found in quadratic equations. It aids in the determination of an equation's solution.