Got Feedback?
Got Feedback?

Found a bug? Have a suggestion? Fill the form below and we'll take a look!





    X

    Discriminant Calculator

    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.

    Please enter parameters:

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

    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.

    • Embed Calculator Widget
    • Direct URL
    • Html Link

    Embed Widget Code.

    Direct URL