Quadratic Equation Solver
Solve equations in the form ax² + bx + c = 0
Understanding Polynomial Equations
A polynomial equation is an equality involving a polynomial. The most common type encountered in algebra is the quadratic equation, which takes the standard form:
ax² + bx + c = 0
Here, x represents the unknown variable, while a, b, and c are numerical coefficients. The coefficient a must not be zero for the equation to remain quadratic.
The Quadratic Formula
To find the roots (solutions) for x, we use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
This formula calculates the points where the parabola represented by the equation crosses the x-axis.
The Discriminant
The term inside the square root, b² – 4ac, is known as the discriminant (Δ). It determines the nature of the roots:
- Δ > 0: There are two distinct real roots.
- Δ = 0: There is exactly one real root (a repeated root).
- Δ < 0: There are no real roots; instead, there are two complex roots involving imaginary numbers.
How to Use the Calculator
Simply enter the values for coefficients a, b, and c into the input fields above. Click "Calculate Roots" to see the solutions for x. The calculator handles both real and complex results automatically.