Class 10 Maths - BIHAR
Polynomials
The Polynomials chapter in Class 10 Mathematics is a fundamental building block of algebra. It covers the geometric meaning of zeroes of a polynomial, the relationship between zeroes and coefficients of quadratic and cubic polynomials, and the division algorithm for polynomials. Mastering this chapter is essential for Bihar (BSEB) board exams as it carries significant weightage in both objective and subjective sections. Students learn how algebraic expressions behave graphically and algebraically, which lays the groundwork for solving quadratic equations and coordinate geometry in later chapters.
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.
Geometric 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 any 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).
Formation of Quadratic Polynomial
A quadratic polynomial can be directly formed using the formula when its sum of zeroes (S) and product of zeroes (P) are given: x^2 - Sx + P.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 10 Mathematics board exam, the chapter 'Polynomials' typically carries around 6 to 8 marks. Questions frequently appear as 1-mark objective multiple-choice questions (finding zeroes from graphs or values), 2-mark short answer questions (finding zeroes and verifying relationships), and occasionally 3 to 5-mark long answer questions involving the division algorithm.
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 exponents of the variables must be non-negative integers.
How can I find the number of zeroes from a given graph?
Count the total number of times the given curve intersects or touches the x-axis. Each intersection point represents one real zero of that polynomial.
Is the Division Algorithm for polynomials important for the BSEB board exam?
Yes, questions asking to find all other zeroes of a polynomial when two of its zeroes are given using the division algorithm are very common in long-answer sections.
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