Quadratic Equation Calculator
Solve quadratic equations in the form ax² + bx + c = 0. Get real roots, complex roots, and detailed solution steps.
Solutions (Roots)
Discriminant (Δ): -
Nature of Roots: -
Quadratic Formula: x = (-b ± √Δ) / 2a
where Δ = b² - 4ac
-
How to use the Quadratic Equation Calculator
- Enter coefficients a, b and c (a cannot be 0).
- Check the equation preview.
- Click Solve.
- Read the discriminant, the nature of roots and both roots with steps.
Formula used
Worked example
Solve x² − 5x + 6 = 0
a = 1, b = −5, c = 6
Δ = 25 − 24 = 1, √Δ = 1
x = (5 ± 1) ÷ 2, so x = 3 or x = 2
What the discriminant tells you
If Δ > 0 there are two different real roots and the parabola crosses the x-axis twice. If Δ = 0 there is one repeated root and the graph just touches the axis. If Δ < 0 the roots are complex conjugates and the graph does not meet the x-axis. Quadratics model projectile motion, area problems and profit curves, and are a core topic in Class 10 maths.
Tips for accurate results
- Move all terms to one side so the equation equals 0.
- Enter negative coefficients with a minus sign.
- Check roots by substituting them back.
Frequently Asked Questions
An equation of the form ax² + bx + c = 0 with a ≠ 0.
Yes, when the discriminant is negative.
−b/a; the product is c/a.
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Content reviewed by Vinod, Easy Smart Calculator · Last updated October 2026
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)