Algebra Calculators
Quadratic Equation Solver
Find the roots of any polynomial of degree 2 instantly.
x² +
x +
= 0
Solutions (Roots)
The Quadratic Formula
A quadratic equation is a second-order polynomial equation in a single variable x, with the standard form ax² + bx + c = 0, where a ≠ 0.
To find the roots (the points where the curve crosses the x-axis), we use the universal quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
The Discriminant
The part underneath the square root, b² - 4ac, is called the discriminant (D). It tells you the nature of the roots:
- If D > 0: There are two distinct real roots.
- If D = 0: There is exactly one real root (a repeated root).
- If D < 0: There are two complex/imaginary roots.