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Class X Mathematics

Chapter 4: Quadratic Equations

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

Quadratic Equation Calculator

Solve quadratic equations of the format ax^2 + bx + c = 0, calculating root coordinates and discriminants.

Live Solver

Adjust Inputs

1
-5
6

Calculated Results

First Root (x1)
3
Second Root (x2)
2
Discriminant (D)
1

Student Solver & Visualizer Guide

Real-time calculations

Step-by-step solving

1. Note standard quadratic format: ax² + bx + c = 0
- Coefficients: a = 1, b = -5, c = 6
2. Solve the Discriminant (D) to evaluate roots properties:
- D = b² - 4ac
- D = (-5)² - 4(1)(6) = 25 - 24 = 1
3. Discriminant D > 0: Two distinct real roots exist.
4. Substitute into quadratic formula: x = [-b ± sqrt(D)] / 2a
- x = [5 ± sqrt(1)] / 2
- x1 = (5 + 1.00) / 2 = 3
- x2 = (5 - 1.00) / 2 = 2

Student-friendly explanations

"A quadratic equation represents a parabola (a smooth U-shaped curve). The coefficients determine how wide the curve is, and the roots represent the exact places where this curved line intersects the horizontal x-axis floor! Here, the roots are at **3** and **2**."

Visual explanations

PARABOLA SLOPE CURVE (y = ax² + bx + c):
    \     /     a = 1 (parabola opens upwards)
     \___/      Roots: x1 = 3, x2 = 2
  ─────┼┼─────  Discriminant: D = 1