Discriminant Calculator
Determine the nature of roots of a quadratic.
Formula first
Overview
The discriminant is a specific algebraic expression derived from the coefficients of a quadratic equation, typically found under the radical in the quadratic formula. It is used to determine the nature and number of roots for a quadratic polynomial without requiring the full solution of the equation.
Symbols
Variables
a = Coefficient a, b = Coefficient b, c = Coefficient c, = Discriminant
Apply it well
When To Use
When to use: Use this formula when you need to categorize the solutions of a quadratic equation of the form ax² + bx + c = 0. It is the primary tool for determining if roots are real or complex, and whether they are distinct or repeated.
Why it matters: In fields like physics and engineering, the discriminant identifies the behavior of physical systems, such as whether a mechanical system will oscillate or return to equilibrium. It also dictates the geometry of a parabola relative to the x-axis in coordinate mathematics.
Avoid these traps
Common Mistakes
- Squaring negative b incorrectly.
- Forgetting the minus sign.
One free problem
Practice Problem
Calculate the discriminant for the quadratic equation 2x² - 5x + 3 = 0 to determine its root nature.
Solve for:
Hint: Square the 'b' value first, then subtract the product of 4, 'a', and 'c'.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Discriminant
- Britannica: Discriminant
- Atkins' Physical Chemistry
- Halliday, Resnick, and Walker, Fundamentals of Physics
- Edexcel A-Level Mathematics — Pure 1 (Quadratics)