Quadratic Equation Calculator Online - Solve Equations Instantly
Solve any quadratic equation (ax² + bx + c = 0) quickly with step-by-step solutions using our calculator.
Quadratic Equation
Enter coefficients for ax² + bx + c = 0
x² - 5x + 6 = 0
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Solution
Roots and properties of the quadratic equation
Roots:
x₁ =0
Properties:
Discriminant (Δ):0.0000
Vertex:(0.0000, 0.0000)
Axis of Symmetry:x = 0.0000
Opens:Upward
Step-by-Step Solution:
1. Identify: a = 1, b = -5, c = 6
2. Calculate discriminant: Δ = b² - 4ac = -5² - 4(1)(6) = 0
3. Apply quadratic formula:
x = (--5 ± √0) / (2 × 1)
4. x₁ = (--5 + √0) / 2 = 0
5. x₂ = (--5 - √0) / 2 = 0
Understanding Quadratic Equations
A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where:
- a is the coefficient of x² (cannot be zero)
- b is the coefficient of x
- c is the constant term
The Quadratic Formula
The quadratic formula x = (-b ± √(b² - 4ac)) / 2a provides the solution to any quadratic equation.
The Discriminant
The discriminant (Δ = b² - 4ac) determines the nature of the roots:
- Δ > 0: Two distinct real roots
- Δ = 0: One repeated real root
- Δ < 0: Two complex conjugate roots
Applications of Quadratic Equations
Physics & Engineering
- Projectile motion calculations
- Optimization problems
- Circuit analysis
- Structural engineering
Business & Economics
- Profit maximization
- Cost analysis
- Revenue optimization
- Break-even analysis