Polynomials is the second chapter in the NCERT Maths textbook for Class 10. It introduces algebraic expressions known as polynomials and their various properties.
Key Concepts
- Polynomials: Algebraic expressions containing one or more terms with non-negative integral exponents.
- Types of Polynomials: Based on the degree, polynomials are classified as linear, quadratic, cubic, etc.
- Zeroes of a Polynomial: The values of the variable for which the polynomial becomes zero.
- Relationship Between Zeroes and Coefficients: The connection between the coefficients of a polynomial and its zeroes.
- Division Algorithm for Polynomials: A method to divide one polynomial by another.
Important Points
- The graph of a quadratic polynomial is a parabola.
- The number of zeroes of a polynomial is less than or equal to its degree.
- The division algorithm states that Dividend = Divisor × Quotient + Remainder.
Exercise 2.1
1. The graphs of y = p(x) are given below for some polynomials p(x). Find the number of zeroes of p(x) in each case.
Ans :
Exercise 2.2
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:
(i) x2 – 2x – 8
(ii) 4s2 – 4s + 1
(iii) 6x2 – 3 – 7x
(iv) 4u2 + 8u
(v) t2 – 15
(vi) 3x2 – x – 4
Ans :
