Quadratic Equations
Kerala Board · Class 10 · Mathematics
Quick revision notes for Quadratic Equations — Kerala Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction and Standard Form
- A quadratic equation in variable x is of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0
- The coefficient 'a' cannot be zero, otherwise it becomes a linear equation
- Any equation that can be reduced to the form ax² + bx + c = 0 is a quadratic equation
Solution by Factorization
- If ax² + bx + c can be factored as (px + q)(rx + s) = 0, then roots are x = -q/p and x = -s/r
- For factorization, find two numbers whose sum equals b and product equals ac
- Split the middle term using these two numbers, then factor by grouping
Solution by Completing the Square
- Rearrange equation so that constant term is on the right side
- Add (b/2a)² to both sides to make left side a perfect square
- Take square root of both sides and solve for x
Quadratic Formula
- Universal formula that works for all quadratic equations
- Derived by completing the square on the general form ax² + bx + c = 0
- Gives exact roots regardless of whether they are rational or irrational
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Quadratic Equations covers several key topics that are frequently asked in Kerala Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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