Class 10th Mathematics - Quadratic Equations

Quadratic Equations - Class 10th Mathematics

Quadratic equations are polynomial equations of degree 2, essential for advanced mathematics.

Standard Form

A quadratic equation is of the form: ax² + bx + c = 0, where a ≠ 0

Methods of Solving

1. Factorization Method: Factor the quadratic expression and set each factor to zero
2. Completing the Square: Transform the equation into perfect square form
3. Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a

Nature of Roots

Based on discriminant (D = b² - 4ac):

• D > 0: Two distinct real roots
• D = 0: One real root (repeated)
• D < 0: No real roots (complex roots)

Practice Problems

1. Solve: x² - 5x + 6 = 0
2. Find the nature of roots of 2x² + 3x + 1 = 0
3. Solve using quadratic formula: 3x² - 2x - 1 = 0