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Polynomials

Gujarat Board · Class 10 · Mathematics

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

45 questions28 flashcards5 concepts

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A labeled diagram illustrating the general form of a polynomial, distinguishing between real and complex polynomials by highlighting the nature of coefficients and variables. Also includes the definit
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Key Topics to Revise

1

Types of Polynomials – A Quick Recall

  • A polynomial in one variable x is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where aₙ ≠ 0 and all coefficients are real numbers.
  • The highest power of the variable in a polynomial is called its DEGREE.
  • Degree 1 → Linear Polynomial (e.g., 2x + 3)
2

Zeroes of a Polynomial

  • A real number k is called a ZERO of polynomial p(x) if p(k) = 0.
  • To find if k is a zero, substitute x = k into the polynomial and check if the result is 0.
  • Example: For p(x) = x² - 3x - 4, p(-1) = (-1)² - 3(-1) - 4 = 1 + 3 - 4 = 0. So -1 is a zero.
3

Geometrical Meaning of Zeroes of a Polynomial

  • The graph of y = ax + b (linear polynomial) is a STRAIGHT LINE that intersects the x-axis at exactly one point: (-b/a, 0). This x-coordinate is the zero.
  • The graph of y = ax² + bx + c (quadratic polynomial) is a PARABOLA.
  • If a > 0, the parabola opens UPWARD (∪ shape).
4

Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

  • For a quadratic polynomial p(x) = ax² + bx + c with zeroes α (alpha) and β (beta):
  • Sum of zeroes: α + β = -b/a = -(coefficient of x) / (coefficient of x²)
  • Product of zeroes: αβ = c/a = (constant term) / (coefficient of x²)

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Full Notes

Key Concepts

A polynomial in one variable xThe degree of a polynomialPolynomials are named based on theirIf p(x) is a polynomialA real number k is called

Frequently Asked Questions

What are the important topics in Polynomials for Gujarat Board Class 10 Mathematics?
Key topics in Polynomials include Polynomials - Complete Chapter Overview, Problem-Solving Strategy for Finding Zeroes of Polynomials, Polynomials – Complete Chapter Overview. These are the concepts Gujarat Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Polynomials — Gujarat Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 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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