द्विघात सूत्र कैलकुलेटर
The detailed guide below is currently available in English.
Reading the discriminant
The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a succeeds for every quadratic, and the piece under the square root — the discriminant b² − 4ac — predicts the answer’s shape before you compute it. A positive discriminant gives two different real roots, exactly zero gives one root repeated, and a negative discriminant gives a complex-conjugate pair with no real solutions, since square roots of negatives are not real. The formula works through completing the square: divide through by a, shift the constant, and solve for the squared term.
अक्सर पूछे जाने वाले प्रश्न
What does the vertex tell me?
It is the turning point of the parabola y = ax² + bx + c, sitting on the axis of symmetry x = −b ÷ 2a. For a > 0 the parabola opens upward and the vertex is the minimum; for a < 0 it is the maximum.
Why do complex roots come in pairs?
A quadratic with real coefficients cannot have exactly one complex root — its conjugate must also be a root, so they appear as p + qi and p − qi sharing the same real part and opposite imaginary parts.