SEBA Class 10 Maths NCERT Solutions – Chapter 2 Polynomials (Exercise 2.1) (Assam SCERT Syllabus 2025-2026 Covered)
In this solution, we provide a detailed and step-by-step explanation of Exercise 2.1 from Chapter 2 – Polynomials as per the SEBA Class 10 Mathematics NCERT syllabus, which aligns with the Assam SCERT curriculum for 2025-2026. This exercise focuses on the fundamental concepts of polynomials, including types of polynomials, degree, coefficient, and zeroes of a polynomial. Our solutions are designed to help students develop a clear understanding of algebraic expressions, ensuring they can solve problems efficiently and accurately. With well-structured explanations, important formulas, and solved examples, this guide will be highly beneficial for students preparing for their exams. Stay connected with Digital Pipal Academy for more such comprehensive solutions and study resources.
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Class 10 Maths NCERT Solutions – Chapter 2 Polynomials (Exercise 2.1)
In this exercise, we will analyze the number of zeroes of a polynomial by observing its graphical representation. The number of zeroes of a polynomial corresponds to the number of times its graph intersects the x-axis.
Question 1:
The graphs of for different polynomials are given in the figures below. Find the number of zeroes of in each case.
Solution:
We determine the number of zeroes by counting the intersections of the graph with the x-axis:
I. The graph does not intersect the x-axis.
Number of zeroes = 0.
II. The graph touches the x-axis at one point.
Number of zeroes = 1.
III. The graph crosses the x-axis at three points.
Number of zeroes = 3.
IV. The graph crosses the x-axis at two points.
Number of zeroes = 2.
V. The graph crosses the x-axis at four points.
Number of zeroes = 4.
VI. The graph crosses the x-axis at three points.
Number of zeroes = 3.
Conclusion:
- If a polynomial graph does not meet the x-axis, it has zero real roots.
- If it touches or crosses the x-axis, the number of zeroes corresponds to the number of intersections.
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