Arbitrary Constant Calculator

This calculator computes the value of a quadratic equation with an arbitrary constant as the coefficient of \(x^2\).

Input Parameters

Calculation Results

Calculation Formula

The quadratic equation is: \(ax^2 + bx + c = 0\)

Where:
\(a\): Coefficient of \(x^2\) (Arbitrary Constant)
\(b\): Coefficient of \(x\) (Linear term)
\(c\): Constant term

Results

Discriminant (Δ):

-

Roots:

-

Arbitrary Constant Calculator Calculator Usage Guide

Learn how to use the Arbitrary Constant Calculator calculator and its working principles

How to Use the Calculator

  1. Enter the coefficient of \(x^2\) (a), the coefficient of \(x\) (b), and the constant term (c) in the input fields.
  2. Click the "Calculate" button to compute the discriminant and the roots of the quadratic equation.
  3. The discriminant and the roots will be displayed in the results section.

Understanding the Results

The discriminant (Δ) is calculated using the formula \(Δ = b^2 - 4ac\). It determines the nature of the roots:

  • If Δ > 0, the equation has two distinct real roots.
  • If Δ = 0, the equation has one real root (a repeated root).
  • If Δ < 0, the equation has two complex roots.

Example

For the quadratic equation \(2x^2 + 4x + 2 = 0\), the inputs would be:

  • a = 2
  • b = 4
  • c = 2

Calculating these, you would find the discriminant and the roots, which in this case would be complex roots.