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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
the polynomial p(x).
2) Quadratic polynomial in x is of the form ax2 + 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
of x.
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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