Quadratic Equations — Syllabus
Maharashtra Board · Class 10 · Mathematics
What Quadratic Equations covers in Maharashtra Board Class 10 Mathematics: 4 topics, for the 2026-27 session. Topics include Quadratic Equation: Basic.
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Topics in Quadratic Equations
1. Quadratic Equation: Basic Idea and Standard Form
- A quadratic equation is an equation involving one variable with highest power 2.
- The general form is ax^2 + bx + c = 0.
- Here, a, b, and c are real numbers and a ≠ 0.
2. Roots of a Quadratic Equation and Factorisation Method
- If p(a) = 0 for a polynomial p(x), then (x - a) is a factor of p(x) and a is a root or solution of p(x) = 0.
- The method of finding linear factors first to solve a quadratic equation is called the factorisation method.
- If product of two numbers is zero, then at least one of them is zero.
3. Completing the Square Method
- This method is useful when factorisation is not easy.
- Add a suitable term so that the expression becomes a perfect square.
- For x^2 + 10x + 2 = 0, complete the square by writing x^2 + 10x + 25 - 25 + 2 = 0.
4. Quadratic Formula and Discriminant
- The quadratic formula gives roots directly for ax^2 + bx + c = 0.
- The roots are written as α and β.
- The formula is X = (-b ± √(b^2 - 4ac)) / 2a.
Key Concepts
Central concept: Quadratic Equations
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