Class 10 Maths - WEST-BENGAL
Polynomials
The chapter Polynomials in Class 10 Mathematics under the West Bengal Board of Secondary Education (WBBSE) introduces students to algebraic expressions with non-negative integer exponents. You will learn about the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of quadratic and cubic polynomials, and the division algorithm for polynomials. This chapter forms the foundation of algebra and graphing in higher classes. Mastering this chapter is essential for scoring well in the Madhyamik board examination, as it regularly features both short-answer and long-answer problem types.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial expression that determines the maximum number of zeroes the polynomial can have.
Geometrical Meaning of Zeroes
The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
Relationship between Zeroes and Coefficients
For a quadratic polynomial ax^2 + bx + c, the sum of zeroes is -b/a and the product of zeroes is c/a.
Division Algorithm for Polynomials
If p(x) and g(x) are two polynomials with g(x) not equal to zero, we can find polynomials q(x) and r(x) such that p(x) = g(x) * q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).
Important Formulas
Board Exam Info
In the West Bengal (WBBSE) Madhyamik Examination, the chapter on Polynomials typically carries around 4 to 6 marks. Questions usually include multiple-choice questions (MCQs), fill-in-the-blanks, very short answer type questions (VSA), and 2-mark or 3-mark problems based on finding zeroes and verifying the relationship between zeroes and coefficients.
Frequently Asked Questions
What is the difference between a polynomial and a general algebraic expression?
Every polynomial is an algebraic expression, but not every algebraic expression is a polynomial. In a polynomial, the powers of the variables must be whole numbers (non-negative integers), and coefficients must be real numbers.
How do I find the number of zeroes from a given graph?
Count the exact number of times the given curve intersects or touches the horizontal x-axis. Each intersection point represents one real zero of that polynomial.
How can I construct a quadratic polynomial if its zeroes are given?
First, calculate the sum and product of the given zeroes. Then, substitute these values into the standard formula: k[x^2 - (sum)x + (product)], where k is a non-zero real number.
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