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Polynomials

Telangana Board · Class 10 · Mathematics

Quick revision notes for Polynomials — Telangana Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

42 questions30 flashcards5 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?
Polynomials covers several key topics that are frequently asked in Telangana Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Polynomials — Telangana Board Class 10 Mathematics?
Understand the core concepts first, then work through the 42 practice questions available for this chapter. Revise formulas and 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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