NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.1#
Welcome to our comprehensive NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.1. This exercise deals with the geometrical meaning of the zeroes of a polynomial. Students learn to read the number of zeroes directly from the graph of a polynomial by counting the number of times the curve crosses or touches the x-axis. These solutions help CBSE Class 10 students build visual understanding of polynomial behaviour.
Key Concept: The zeroes of a polynomial $p(x)$ are the x-coordinates of the points where the graph of $y = p(x)$ intersects or touches the x-axis. The number of zeroes of a polynomial equals the number of times its graph crosses the x-axis.
1. The graphs of $y = p(x)$ are given in the figures below, for some polynomials $p(x)$. Find the number of zeroes of $p(x)$ in each case. #
(i) Graph (i)
The graph of $y = p(x)$ is a straight line that does not intersect the x-axis at any point.
∴ The number of zeroes = 0
(ii) Graph (ii)
The graph of $y = p(x)$ intersects the x-axis at exactly one point.
∴ The number of zeroes = 1
(iii) Graph (iii)
The graph of $y = p(x)$ intersects the x-axis at exactly three points.
∴ The number of zeroes = 3
(iv) Graph (iv)
The graph of $y = p(x)$ intersects the x-axis at exactly two points.
∴ The number of zeroes = 2
(v) Graph (v)
The graph of $y = p(x)$ intersects the x-axis at exactly four points.
∴ The number of zeroes = 4
(vi) Graph (vi)
The graph of $y = p(x)$ intersects the x-axis at exactly three points.
∴ The number of zeroes = 3