NCERT New Syllabus Mathematics

Class: 10

Exercise 2.1

Topic: Polynomials

**Understanding Polynomials: A Key Chapter in Class 10 Mathematics**

Polynomials form a fundamental building block in algebra and are crucial in understanding various higher-level concepts in mathematics. In this chapter of the 10th-grade NCERT syllabus, students will explore how to express algebraic expressions in polynomials and analyze their behavior through various methods. From identifying degrees to solving for roots, this chapter will empower you to solve equations efficiently, laying a strong foundation for future mathematical concepts like calculus and advanced algebra.

1) If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of

2) Quadratic polynomial in x is of the form ax^{2} + bx + c, where a, b, c are real

numbers and a ≠ 0.

3) In general, for a polynomial p(x) of degree n, the graph of y = p(x) intersects

the x-axis at at most n points. Therefore, a polynomial p(x) of degree n has at most n zeroes.

### EXERCISE 2.1

**Q1. The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.**

### Explanation:

1) The graphs of y = p(x) intersects or touches the x-axis when y = 0. The number

of zeroes of the polynomial p(x) corresponds to the values of x where p(x) = 0.

2) To find zeroes, set y = 0 in the equation y = p(x) and solve for all possible values

3) Simply observe how many times the graph intersects or touches the x-axis to

determine the number of zeroes.

### Solution:

**Conclusion: The Power and Elegance of Polynomials**

Polynomials are not just expressions with variables and coefficients – they are the keys to unlocking complex mathematical ideas. From their applications in algebra to their relevance in real-world problems, mastering polynomials equips you with a versatile tool in mathematics. As you progress through this fascinating journey, remember that every equation you solve and every concept you understand builds your foundation for more advanced topics. Embrace the elegance of polynomials and keep solving with curiosity!

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