Quadratic formula Calculator
Solve a quadratic equation ax²+bx+c=0.
Formula first
Overview
The quadratic formula provides the roots of a second-degree polynomial equation in the form ax² + bx + c = 0. It is derived from the algebraic process of completing the square and describes the specific values of the independent variable where the parabola intersects the horizontal axis.
Symbols
Variables
a = Coefficient a, b = Coefficient b, c = Coefficient c, x = Root (one solution)
Apply it well
When To Use
When to use: Use this formula when dealing with a quadratic equation that cannot be easily factored by inspection. It is applicable whenever the equation is expressed in standard form and the leading coefficient 'a' is not zero.
Why it matters: This formula is fundamental in physics for calculating projectile motion and in engineering for optimizing structural designs. It allows for the identification of real or complex solutions, providing essential insight into the behavior of parabolic systems.
Avoid these traps
Common Mistakes
- Wrong sign for -b.
- Computing b²-4ac incorrectly.
One free problem
Practice Problem
Find the larger root of the equation x² - 7x + 10 = 0.
Solve for:
Hint: The discriminant b² - 4ac is equal to 9, which is a perfect square.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Quadratic formula
- Stewart, J. (2015). Calculus: Early Transcendentals. Cengage Learning.
- Halliday, Resnick, Walker - Fundamentals of Physics, 10th Edition
- Britannica: Quadratic equation
- Wikipedia: Quadratic equation
- Standard curriculum — A-Level Pure Mathematics