मुफ्त द्विघात सूत्र कैलकुलेटर
द्विघात समीकरण ax² + bx + c = 0 को हल करें। a, b, c दर्ज करके मूल (रूट) पाएं।
Coefficient of x²
Coefficient of x
Constant term
Root1
3.000000
Discriminant Val1.0000
Vertex X2.5000
Vertex Y-0.2500
सूत्र
How to Use the Quadratic Formula
Formula
x = (-b ± √(b² - 4ac)) / (2a)
For the equation ax² + bx + c = 0
Discriminant (Δ = b² - 4ac)
Vertex
The vertex of the parabola is at x = -b/(2a), y = f(-b/(2a)).
हल किया गया उदाहरण
Solve x² - 5x + 6 = 0 (a=1, b=-5, c=6).
- 01Discriminant = (-5)² - 4(1)(6) = 25 - 24 = 1
- 02Since Δ > 0, there are two distinct real roots
- 03x₁ = (5 + √1) / 2 = 6 / 2 = 3
- 04x₂ = (5 - √1) / 2 = 4 / 2 = 2
- 05Vertex: x = 5/2 = 2.5, y = (2.5)² - 5(2.5) + 6 = -0.25
अक्सर पूछे जाने वाले प्रश्न
What is the quadratic formula?
The quadratic formula x = (-b ± √(b²-4ac)) / (2a) finds the solutions (roots) of any quadratic equation ax² + bx + c = 0.
What does the discriminant tell us?
The discriminant (b²-4ac) tells you the nature of the roots: positive = 2 real roots, zero = 1 repeated root, negative = no real roots (2 complex roots).
What if the discriminant is negative?
If the discriminant is negative, the equation has no real solutions. The roots are complex numbers. This calculator shows the real part when the discriminant is negative.
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