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Polynomials — Revision Notes

Gujarat Board · Class 10 · Mathematics

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

45 questions28 flashcards10 formulas & key relations5 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 Types of Polynomials – A Quick Recall, Zeroes of a Polynomial, Geometrical Meaning of Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Quadratic Polynomial. Study these first, then practise questions on each for the Gujarat Board Class 10 board exam.
How should I revise Polynomials for the Gujarat Board Class 10 board exam?
Learn the core ideas first, then work through the 45 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 Gujarat Board Class 10 Mathematics Revision Notes

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