Quadratic Equation Calculator
Solve quadratic equations in the form ax² + bx + c = 0. Get real roots, complex roots, and detailed solution steps.
x² + 5x + 6 = 0
Solutions (Roots)
Root 1 (x₁)
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Root 2 (x₂)
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📐 Analysis:
Discriminant (Δ): -
Nature of Roots: -
Quadratic Formula: x = (-b ± √Δ) / 2a
where Δ = b² - 4ac
Discriminant (Δ): -
Nature of Roots: -
Quadratic Formula: x = (-b ± √Δ) / 2a
where Δ = b² - 4ac
📋 Solution Steps:
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-
Understanding Quadratic Equations
Standard Form: ax² + bx + c = 0, where a ≠ 0
Solutions (Roots): Values of x that make the equation equal to zero.
Discriminant (Δ): Δ = b² - 4ac determines the nature of roots.
Discriminant Analysis
- Δ > 0: Two distinct real roots
- Δ = 0: One repeated real root (perfect square)
- Δ < 0: Two complex conjugate roots
Examples
- x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0 → x = -2 or x = -3
- x² - 4 = 0 → (x - 2)(x + 2) = 0 → x = 2 or x = -2
- x² + 1 = 0 → x = ±i (complex roots)