Class 10 Maths - ODISHA
Polynomials
The Polynomials chapter in Class 10 Mathematics for Odisha BSE students builds upon algebraic expressions learned in earlier classes. Students will explore the geometrical meaning of zeroes of a polynomial, the relationship between zeroes and coefficients of quadratic polynomials, and the division algorithm for polynomials. This chapter is fundamental for higher-level algebra and consistently carries significant weight in the BSE Odisha board examinations, featuring both objective and short-answer questions that test conceptual clarity and problem-solving skills.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree, which determines the maximum number of zeroes the polynomial can have.
Geometrical Meaning of Zeroes
The zeroes of a polynomial are the x-coordinates of the points where the graph of the polynomial equation intersects the x-axis.
Relationship between Zeroes and Coefficients
For a quadratic polynomial ax squared + bx + c, the sum of zeroes equals -b/a and the product of zeroes equals 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) multiplied by q(x) plus r(x).
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 10 Mathematics board exam, Polynomials typically carries around 5 to 8 marks. Questions usually include multiple-choice questions (MCQs) identifying graphs, finding zeroes of quadratic polynomials, verifying the relationship between zeroes and coefficients, and applying the division algorithm.
Frequently Asked Questions
How do I find the zeroes of a quadratic polynomial?
You can find the zeroes by splitting the middle term to factorize the polynomial and then setting each factor equal to zero.
What is the difference between a zero of a polynomial and the root of an equation?
A zero of a polynomial p(x) is the value of x where p(x) = 0, whereas the root refers to a solution of an equation set to zero, though they are numerically the same for polynomial equations.
Is the division algorithm compulsory for the BSE Odisha board exam?
Yes, long division of polynomials and verifying the division algorithm are frequently asked as 2 or 3-mark questions in the board exam.
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