NCERT Class 10 Maths – Exercise 2.1 Solutions

NCERT Class 10 Maths

Chapter 2 – Polynomials | Exercise 2.1

(Rationalized Syllabus 2025-26)

💡 Key Concept: Geometric Meaning of Zeroes

For any polynomial $p(x)$, the graph of $y = p(x)$ intersects the X-axis at certain points.

  • Rule: The number of zeroes of the polynomial $p(x)$ is equal to the number of points where the graph of $y = p(x)$ intersects or touches the X-axis.
Q1

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)
The graph is a straight line parallel to the X-axis. It does not intersect the X-axis at any point.
✔️ Number of zeroes = 0
(ii)
The graph intersects the X-axis at exactly one point.
✔️ Number of zeroes = 1
(iii)
The graph intersects the X-axis at three distinct points.
✔️ Number of zeroes = 3
(iv)
The graph (a parabola) intersects the X-axis at two points.
✔️ Number of zeroes = 2
(v)
The graph intersects the X-axis at four points.
✔️ Number of zeroes = 4
(vi)
The graph intersects the X-axis at one point and touches it at two other points. Total points of contact = 3.
✔️ Number of zeroes = 3
🎉 Exercise 2.1 Completed | Chapter 2 Polynomials
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