Quadratic Equation Calculator

ℹ️ What is Quadratic Equation Calculator?

A quadratic equation calculator finds the roots (solutions) of any equation in the form ax² + bx + c = 0. It uses the quadratic formula to determine whether the equation has two real roots, one repeated root, or two complex roots.

📐 Formula

✏️ Worked Example

1. 1Discriminant = (−5)² − 4(2)(−3) = 25 + 24 = 49
2. 2√49 = 7
3. 3x₁ = (5 + 7) / (2×2) = 12/4 = 3
4. 4x₂ = (5 − 7) / (2×2) = −2/4 = −0.5
5. 5Verify x₁: 2(3)² − 5(3) − 3 = 18 − 15 − 3 = 0 ✓

💡 How to Interpret Results

• ▸Discriminant > 0: two distinct real roots — the parabola crosses the x-axis at two points.
• ▸Discriminant = 0: one repeated real root (double root) — the parabola is tangent to the x-axis.
• ▸Discriminant < 0: no real roots, two complex conjugate roots — the parabola doesn't cross x-axis.
• ▸The vertex of the parabola is at x = −b/(2a), y = c − b²/(4a).
• ▸The roots are symmetric about x = −b/(2a) — the axis of symmetry.

❓ Frequently Asked Questions

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