A discriminant calculator can be used for finding the quadratic equation's discriminant value for the specified coefficients.
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 \(Δ\).
\(∴ Δ = b^2 – 4ac \)
Calculations are made quicker and easier using the online discriminant calculator tool from Mathematics Master, which shows the result in a split second.
|Graphs of \( y = ax^2 + bx + c \)||Discriminant||Number of types and solutions|
|Discriminant is negative||No x-intercepts
Two imaginary solutions
|Discriminant is zero||One x-intercept
One Root (a double root)
One real solution
|Discriminant is positive||Two x-intercepts
Two real solutions
The discriminant describes the characteristics of quadratic equations’ roots. The equations can distinguish between possible types of answers, including:
The value that assists us in identifying the different types of solutions when using the quadratic formula is known as the “discriminant.” It is a unique function of a quadratic equation’s coefficient whose value provides details about its roots.
The discriminant distinguishes three distinct sorts 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
\( =b^2-4ac \)
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
\( =b^2-4ac \)
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
\( =b^2-4ac \)
Take the actions listed below to use the discriminant calculator:
What do the discriminants (Δ) tell us?
With the discriminant, we can determine if there are two solutions, one solution, or no solutions.
How many solutions are possible if the discriminant is more significant than zero?
If the square is perfect, there are two solutions (2 real solutions); otherwise, there are two rational roots and two irrational roots.
Why is the discriminant value in a quadratic equation significant?
The discriminant value reveals the characteristics of the quadratic equation’s roots. The quadratic equation can have real or complex roots. It aids in determining an equation’s solution.
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