Quadratic Equation Solver with Step-by-Step Formula (कैलकुलेटर) — मुफ़्त ऑनलाइन टूल और फॉर्मूला
Solves quadratic polynomials ax² + bx + c = 0, determining the discriminant, vertex coordinates, and real or complex roots with algebraic steps.
Nature: Two Distinct Real Roots
फॉर्मूला और गणना की विधि
Solves second-degree polynomial equations ax² + bx + c = 0, determining real, repeated, or complex conjugate roots alongside parabola vertex coordinates and axis of symmetry.
वेरिएबल परिभाषाएँ और माप इकाइयाँ
Solving x² − 5x + 6 = 0
Finding roots and vertex coordinates for a = 1, b = -5, c = 6.
Algebraic Classification via the Discriminant D
When D > 0, the parabola intersects the x-axis at two distinct real coordinates. When D = 0, the vertex is tangent to the x-axis, creating a single repeated real root.
When D < 0, the parabola never crosses the x-axis in the Cartesian plane, producing two complex conjugate roots of the form u ± vi, crucial for electrical engineering and resonance damping equations.
Quadratic Equation Solver with Step-by-Step Formula (कैलकुलेटर) से जुड़े अक्सर पूछे जाने वाले प्रश्न
What happens if a = 0?
If a = 0, the equation reduces to a linear equation bx + c = 0 with a single root x = -c/b.
What is the axis of symmetry of a parabola?
The vertical line passing through the vertex, given by x = -b / (2a).
संबंधित ऑनलाइन कैलकुलेटर
Quadratic Equation Solver with Step-by-Step Formula (कैलकुलेटर) के साथ अक्सर संदर्भित अन्य कैलकुलेटर।
Matrix Determinant (2×2 & 3×3) कैलकुलेटर
Computes determinants for 2×2 and 3×3 square matrices with explicit Laplace cofactor expansions and geometric singularity checks.
Area & Perimeter Geometry (All Shapes) कैलकुलेटर
Computes geometric planar surface area and boundary perimeter for Rectangles, Circles, Triangles, Squares, and Trapezoids.
प्रतिशत कैलकुलेटर
किसी संख्या का प्रतिशत निकालना, दो संख्याओं के बीच प्रतिशत परिवर्तन (वृद्धि/कमी) और परीक्षा अंकों का प्रतिशत सेकंडों में ज्ञात करें।