Quadratic Equation Solver

Find the Roots of Quadratic Equations

Solve quadratic equations of the form ax² + bx + c = 0 instantly. Our calculator uses the well-known quadratic formula to find the roots (or solutions) of the equation. These roots represent the x-intercepts of the parabola, i.e., where the curve crosses the x-axis.

The Quadratic Formula Explained

The formula for finding the roots of a quadratic equation is: x = [-b ± √(b²-4ac)] / 2a

• a, b, c: These are the numerical coefficients from your equation.
• b²-4ac: This part is called the discriminant. Its value determines the nature of the roots:
  • If positive, there are two distinct real roots.
  • If zero, there is exactly one real root.
  • If negative, there are no real roots (the roots are complex).

How to Use the Calculator

1. Identify Coefficients: From your equation ax² + bx + c = 0, identify the values for a, b, and c.
2. Enter Coefficients: Input the values for a, b, and c into the respective fields.
3. Solve: The calculator will apply the quadratic formula and display the real roots.

Real-World Example

Consider the equation 2x² - 5x - 3 = 0.

• a = 2
• b = -5
• c = -3

Calculation:

• Discriminant: (-5)² - 4(2)(-3) = 25 + 24 = 49
• Roots: [ -(-5) ± √49 ] / (2*2) = [ 5 ± 7 ] / 4
• x₁ = (5 + 7) / 4 = 12 / 4 = 3
• x₂ = (5 - 7) / 4 = -2 / 4 = -0.5

Frequently Asked Questions (FAQ)

• What if 'a' is 0? If 'a' is 0, the equation is not quadratic; it is a linear equation (bx + c = 0). This calculator is only for quadratic equations where 'a' is non-zero.
• What does 'No real roots' mean? It means the parabola representing the equation never crosses the x-axis. The solutions involve imaginary numbers, which this calculator does not compute.
• Can I enter decimals or fractions for coefficients? Yes, the calculator can handle decimal coefficients.