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Revision Notes
Quadratic Equations and Linear Inequalities — Revision Notes
NIOS · Class 12 · Mathematics
Quadratic Equations and Linear Inequalities revision notes for NIOS Class 12 Mathematics: 4 topics in quick points.
45 questions25 flashcards6 formulas & key relations5 concepts
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Key Topics to Revise
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1. Quadratic Equations — Basics and Roots
- A quadratic equation has the standard form ax² + bx + c = 0, where a ≠ 0. Here 'a' is the leading coefficient, 'b' is the middle coefficient, and 'c' is the constant term.
- A root (or solution) is a value of x that satisfies the equation when substituted into it.
- Every quadratic equation has EXACTLY 2 roots (counting multiplicity) — this follows from the Fundamental Theorem of Algebra.
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2. Solving Quadratic Equations by Factorization
- Factorization method involves splitting the middle term (bx) into two parts whose product equals a × c and whose sum equals b.
- After splitting, group the terms, take common factors, and express as a product of two linear factors.
- Set each factor equal to zero and solve — this gives the two roots.
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3. Solving Quadratic Equations by Quadratic Formula (Sridharacharya's Formula)
- The quadratic formula gives the roots of ax² + bx + c = 0 directly using the coefficients a, b, c.
- The discriminant D = b² - 4ac determines the NATURE of roots BEFORE actually computing them.
- If D > 0: two distinct real roots. If D = 0: two equal real roots (each equal to -b/2a). If D < 0: two complex conjugate roots.
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4. Relation Between Roots and Coefficients
- For the quadratic equation ax² + bx + c = 0 with roots α and β: Sum of roots = α + β = -b/a, Product of roots = αβ = c/a.
- These relations allow us to find expressions involving α and β WITHOUT actually solving for α and β separately.
- To form a new quadratic equation with given roots p and q: x² - (p + q)x + pq = 0.
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Full NotesKey Concepts
A polynomial equation of the secondA valueA technique to solve quadratic equationsA universal formula to find rootsThe expression D = b²
Frequently Asked Questions
What are the important topics in Quadratic Equations and Linear Inequalities for NIOS Class 12 Mathematics?
Key topics in Quadratic Equations and Linear Inequalities include Quadratic Equations — Basics and Roots, Solving Quadratic Equations by Factorization, Solving Quadratic Equations by Quadratic Formula (Sridharacharya's Formula), Relation Between Roots and Coefficients. Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Quadratic Equations and Linear Inequalities for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Quadratic Equations and Linear Inequalities. Revise definitions regularly and use flashcards for quick recall before the exam.
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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