Discriminant Calculator calculates the value of discriminant for any given quadratic equation if the values of $a, b, c$ are entered in the block provided.

The Discriminant is a number got from the quadratic equation which tells about the nature of the roots of quadratic equation.

A quadratic equation is an equation of the form
 Quadratic EquationWhere $a,\ b$ and $c$ are values and $a \neq 0$. 

Discriminant is given by formula
Formula for Discriminant

If $b^{2} - 4ac > 0$ we get two solutions of real numbers

If $b^{2} - 4ac$ = $0$ we get one solution which is a real number

If $b^{2} - 4ac < 0$ we get two solutions of rots of imaginary numbers.
Steps for solving Discriminant:
Step 1:

Read the given problem and observe whether the given equation is of the form

$ax^{2} + bx + c$

Write down the values of $a, b$ and $c$.
Step 2:

The discriminant formula is given by

$D$ = $b^{2} - 4ac$

Substitute the values in this formula and get the answer.
Below are given some solved examples based on the discriminant which may be helpful for you.

Solved Examples

Question 1: Find the discriminant of the following equation: x2 - 2x + 1
Solution:
 
Given: x2 - 2x + 1 is a quadratic equation
Here a = 1, b = -2 and c = 1
The discriminant is given by
D = b2 - 4ac
   = (-2)2 - 4(1)(1)
   = 4 - 4 = 0.
The quadratic equation will be having only one real root.
 

Question 2: Find the discriminant of the following equation: 4x2 - 5x + 1
Solution:
 
Given: 4x2 - 5x + 1 is a quadratic equation
Here a = 4, b = -5 and c = 1
The discriminant is given by
D = b2 - 4ac = (-5)2 - 4(4)(1)
   = 25 - 16 = 9.
This quadratic equation will be having two real solutions.
 

Question 3: Find the discriminant of the following equation: 3x2 + x + 2
Solution:
 
Given: 3x2 + x + 2 is a quadratic equation
Here a = 1, b = -2 and c = 1
The discriminant is given by
D = b2 - 4ac
   = (1)2 - 4(3)(2)
   = 1 - 24 = -23.
The quadratic equation will be having two imaginary roots.