Quadratic Equations
Maharashtra Board · Class 10 · Mathematics
Quick revision notes for Quadratic Equations — Maharashtra Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Standard Form and Basic Concepts
- A quadratic equation is an equation involving one variable with maximum power 2
- General form: ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0
- The term 'a' is coefficient of x², 'b' is coefficient of x, and 'c' is the constant term
Methods of Solving Quadratic Equations
- Factorization method: Express as (x - α)(x - β) = 0
- Completing the square: Convert ax² + bx + c into perfect square form
- Quadratic formula: Universal method that works for all quadratic equations
Nature of Roots and Discriminant
- Discriminant Δ = b² - 4ac determines the nature of roots
- If Δ > 0: two distinct real roots
- If Δ = 0: two equal real roots (repeated root)
Relationship Between Roots and Coefficients
- Sum of roots: α + β = -b/a
- Product of roots: αβ = c/a
- These relationships hold regardless of the method used to find roots
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