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Polynomials — Revision Notes

Telangana Board · Class 10 · Mathematics

Polynomials revision notes for Telangana Board Class 10 Mathematics: 4 topics in quick points. Part of the Telangana Board Class 10 Mathematics syllabus.

42 questions30 flashcards10 formulas & key relations5 concepts

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Key Topics to Revise

1

1. What is a Polynomial?

  • A polynomial in x is an algebraic expression containing the sum of a finite number of terms of the form ax^n, where a is a real number, a != 0, and n is a whole number.
  • Terms with negative powers or fractional powers are not polynomials.
  • A polynomial may have one variable or more than one variable, but the chapter focuses on one variable.
2

2. Value of a Polynomial and Zeroes

  • The value of a polynomial p(x) at x = k is written as p(k), found by substituting k for x.
  • A real number k is a zero of a polynomial p(x) if p(k) = 0.
  • For p(x) = x^2 - 2x - 3, the values at x = 3 and x = -1 are 0, so 3 and -1 are zeroes.
3

3. Zeroes of Quadratic Polynomials

  • A quadratic polynomial is of the form ax^2 + bx + c, where a != 0.
  • A quadratic polynomial can have two distinct zeroes, two equal zeroes, or no real zeroes.
  • If the graph of a quadratic polynomial cuts the X-axis at two distinct points, it has two zeroes.
4

4. Zeroes of Cubic Polynomials

  • A cubic polynomial is of the form ax^3 + bx^2 + cx + d, where a != 0.
  • A cubic polynomial has at most three zeroes.
  • The graph of a cubic polynomial can intersect the X-axis at one, two, or three points.

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Full Notes

Key Concepts

A polynomial in x isThe degree is the highest powerA polynomial of degree 1A polynomial of degree 2A polynomial of degree 3

Frequently Asked Questions

What are the important topics in Polynomials for Telangana Board Class 10 Mathematics?
Key topics in Polynomials include What is a Polynomial?, Value of a Polynomial and Zeroes, Zeroes of Quadratic Polynomials, Zeroes of Cubic Polynomials. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How should I revise Polynomials for the Telangana Board Class 10 board exam?
Learn the core ideas first, then work through the 42 practice questions on Polynomials. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Telangana Board Class 10 Mathematics Revision Notes

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