The Discriminant tells about the nature of the roots of quadratic equation. In quadratic equation formula, we have \( b^2 - 4ac \) under root, this is discriminant of quadratic equations.
There are three cases for discriminant:
if \( b^2 - 4ac = 0 \), then the roots of quadratic equations are real and equal.
if \( b^2 - 4ac > 0 \), then the roots are real but not equal
if \( b^2 - 4ac < 0 \), then the roots are not equal and are imaginary.
Discriminant Calculator
What is Discriminant?
Discriminant in math, is a function of coefficients of a polynomial equation. Answers of Discriminant expression can be identified as following:
if \( b^2 – 4ac = 0 \), then we get one real solution.
if \( b^2 – 4ac > 0 \), then we get two real solutions.
if \( b^2 – 4ac < 0 \), then we get two imaginary solutions.
Discriminant Formula:
Formula for finding discriminant is:
= \( b^2 – 4ac \)
Where:
a is the coefficient of x2.
b is the coefficient of x.
c is a constant term.
Results of this formula, tells us how many solutions our quadratic has.
Example of discriminant calculation:
Example 1:
\( x^2 + 6x + 8 = 0 \)
A = 1
B = 6
C = 8
Discriminant:
= \( b^2 – 4ac \)
= \( 6^2 – 4(1)(8) \)
= \( 36 – 32 \)
= \( 4 \)
The number is positive, hence both roots of this equation are real and unequal.
Example 2:
X2 + 4x + 12 = 0
A = 1
B = 4
C = 12
Discriminant:
= \( b^2 – 4ac \)
= \( 4^2 – 4(1)(4) \)
= \( 16 – 48 \)
= \( -32 \)
The number is negative, hence this equation has no real solution.
What does it mean if a discriminant is positive?
If discriminant is higher than zero. It represents that the quadratic equation has two real number solutions. Graphical representation can be seen below:
How to use Discriminant Calculator?
- Enter coefficient values for “a”, “b” and “c” in the above fields.
- Click “Submit”.
- Our discriminant calculator displays the solutions including all the steps and description at the end.
Cases of Discriminant:
In this section, you will learn about Discriminant, how many forms of Discriminant with examples.
There are 3 cases of Discriminant.
Case 1: real and equal:
The discriminant is equal to 0 is known as real and equal.
Example:
= \( x^2 – 4x + 4 \)
= \( a = 1, b = 4, c = 4 \)
= \( b^2 – 4ac \)
= \( 4^2 – 4(1)(2) \)
= \( 16 – 16 \)
= 0
The root are real and equal.
Case 2: real and unequal
The discriminant is greater then 0 is known as real and unequal.
Example:
= \( 4^2 – 10x + 3 \)
= \( a = 4, b = 10, c = 3 \)
= \( b^2 – 4ac \)
= \( 10^2 – 4(4)(3) \)
= \( 100 – 48 \)
= 52
The root are real and unequal.
Case 3: unequal and imaginary
The discriminant is less then 0 is known as unequal and imaginary.
Example:
= \( 4^2 – 4x + 3 \)
= \( a = 4, b = 4, c = 3 \)
= \( b^2 – 4ac \)
= \( 4^2 – 4(4)(3) \)
= \( 16 – 48 \)
= 52
The root are unequal and imaginary.