The Discriminant of The Quadratic Equation Calculator is a powerful tool that computes a vital value used in solving quadratic equations. The formula for the Discriminant (D) is derived from the coefficients of a quadratic equation (ax^2 + bx + c = 0) using the equation:
Discriminant (D) = b^2 – 4ac
Where ‘a’, ‘b’, and ‘c’ represent the coefficients in the quadratic equation. The discriminant (D) serves as a significant determinant of the nature of the equation’s roots or solutions. Here’s what the discriminant can reveal about the roots:
- If D > 0: The equation has two distinct real roots.
- If D = 0: The equation has exactly one real root (a repeated root).
- If D < 0: The equation has two complex (non-real) roots.
This calculation is immensely valuable in determining the behavior of quadratic equations and offers insights into the types of solutions they possess.
General Terms for Quick Reference
Here are some general terms related to quadratic equations that people often search for, making them helpful for quick reference:
| Term | Definition |
|---|---|
| Quadratic Equation | An equation of the form ax^2 + bx + c = 0. |
| Real Roots | Solutions that are real numbers. |
| Complex Roots | Solutions that involve imaginary numbers. |
| Discriminant | The value used to determine the nature of the roots. |
These terms serve as a practical reference for individuals seeking to understand quadratic equations without recalculating each time.
Example of Discriminant of The Quadratic Equation Calculator
Consider the quadratic equation: 3x^2 + 4x – 2 = 0.
Here, ‘a’ = 3, ‘b’ = 4, and ‘c’ = -2.
The discriminant (D) can be calculated as follows:
D = b^2 – 4ac = (4)^2 – 4 * 3 * (-2) = 16 + 24 = 40
As the calculated discriminant is D > 0 (40), this equation has two distinct real roots.
Most Common FAQs
A: When the discriminant is zero, the quadratic equation has exactly one real root, which means it has a repeated root.
A: Yes, if the discriminant is negative, the quadratic equation will have two complex (non-real) roots.
