Quadratic Formula Calculator - Solve ax² + bx + c = 0 Instantly
Solve quadratic equations easily with our step-by-step calculator. Find real and complex roots, calculate the discriminant, and understand the solution process.
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What is the Quadratic Formula?
The quadratic formula is a fundamental algebraic tool used to find the solutions (roots) of any quadratic equation. A quadratic equation is a second-degree polynomial equation in the standard form: ax² + bx + c = 0, where 'x' represents an unknown, and 'a', 'b', and 'c' are constants. The formula ensures you can find the roots even when the equation cannot be easily factored.
The Quadratic Formula
x = [-b ± √(b² - 4ac)] / (2a)To find the roots, you calculate the discriminant first (Δ = b² - 4ac). If the discriminant is positive, you get two real roots. If zero, one real root. If negative, you get complex roots involving 'i'.
Example Calculations
Standard Real Roots
For x² - 5x + 6 = 0: a=1, b=-5, c=6. The discriminant is 1. The roots are x₁=3 and x₂=2.
Complex Roots Case
For x² + 4x + 5 = 0: a=1, b=4, c=5. The discriminant is -4. The roots are complex: -2 + 1i and -2 - 1i.