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Quadratic Equation Solver - Find Roots Calculator
Free quadratic equation solver using the quadratic formula. Find roots, discriminant, and vertex of ax²+bx+c=0 equations instantly.
Quadratic Equation Solver
Solve ax² + bx + c = 0
Solutions
Enter your values to see results
and click the "Calculate" button
What is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0. These equations can have two real solutions, one real solution (repeated root), or two complex solutions depending on the discriminant value.
How to Use This Calculator
- Enter coefficient a (the number before x²)
- Enter coefficient b (the number before x)
- Enter coefficient c (the constant)
- Click Solve to find the roots
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
The discriminant Δ = b² - 4ac determines: Δ > 0: two real roots, Δ = 0: one repeated root, Δ < 0: two complex roots.
Frequently Asked Questions
What does the discriminant tell us?
The discriminant (b² - 4ac) reveals the nature of solutions: positive means two distinct real roots, zero means one repeated root, negative means two complex conjugate roots.
Why can't 'a' be zero?
If a = 0, the equation becomes linear (bx + c = 0), not quadratic. A quadratic equation must have an x² term with a non-zero coefficient.
What is the vertex of a parabola?
The vertex is the highest or lowest point of the parabola. It occurs at x = -b/(2a), and the y-value is found by substituting this x into the equation.
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