Quadratic Equations Notes: Class 10 Maths Chapter 4
Class 10 Maths Chapter 4 Quadratic Equations covers the standard form of a quadratic equation, solving by factorisation, completing the square, the quadratic formula, and the nature of roots using the discriminant.
Overview of Topics & Subtopics (Click to Jump)
1. Quadratic Equations
Short Note:
• A quadratic equation in x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
• A real number α is a root of the quadratic equation if aα² + bα + c = 0; the roots are the same as the zeroes of the corresponding quadratic polynomial.
2. Solution by Factorisation
Short Note:
• If ax²+bx+c can be written as a product of two linear factors, the roots can be found by setting each factor to zero.
3. Solution by Completing the Square & the Quadratic Formula
Short Note:
• Every quadratic equation can be solved by completing the square to express it as (x + k)² = constant.
• Quadratic Formula: For ax²+bx+c=0 (a ≠ 0), x = [−b ± √(b²−4ac)] / 2a.
4. Nature of Roots (Discriminant)
Short Note:
• The discriminant D = b² − 4ac determines the nature of the roots.
• If D > 0: two distinct real roots. If D = 0: two equal real roots. If D < 0: no real roots.