Short Intro
In this post, students can find complete step-by-step solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.1 based on the latest NCERT syllabus. All questions are solved in an easy and exam-oriented format to help students understand the graphical meaning of zeroes of polynomials.
Exercise 2.1 is based on graphs of polynomials and finding the number of zeroes from graphs.
Quick Information Box
| Item | Details |
|---|---|
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Chapter | Polynomials |
| Exercise | 2.1 |
| Main Topic | Zeroes of Polynomial |
Concepts Used (Topics Covered)
- Polynomials
- Linear Polynomial
- Quadratic Polynomial
- Cubic Polynomial
- Zeroes of Polynomial
- Graphical Representation of Polynomial
The exercise explains that zeroes of a polynomial are the x-coordinates where the graph cuts the x-axis.
Important Formulas
Polynomial Form
p(x)=axn+bxn−1+⋯
Zero of Polynomial
p(k)=0
Linear Polynomial
ax+b
Quadratic Polynomial
ax2+bx+c
Questions & Step-by-step Solutions
Question 1
The graphs of y = p(x) are given below. Find the number of zeroes of p(x) in each case.
The number of zeroes of a polynomial is equal to the number of times the graph intersects the x-axis.
(i)
Solution
From the graph, the line is parallel to the x-axis and does not intersect the x-axis.
Therefore,
Number of zeroes = 0
(ii)
Solution
From the graph, the curve intersects the x-axis at one point.
Therefore,
Number of zeroes = 1
(iii)
Solution
The graph cuts the x-axis at two points.
Therefore,
Number of zeroes = 2
(iv)
Solution
The graph intersects the x-axis at two distinct points.
Therefore,
Number of zeroes = 2
(v)
Solution
The graph intersects the x-axis at three points.
Therefore,
Number of zeroes = 3
(vi)
Solution
The graph intersects the x-axis at four points.
Therefore,
Number of zeroes = 4
Important Observation
Key Rule
Number of zeroes = Number of points where graph cuts x-axis
This is the most important concept of Exercise 2.1.
Common Mistakes
- Counting touching points incorrectly
- Confusing y-axis intersections with x-axis intersections
- Missing repeated intersections
- Counting turning points as zeroes
Exam Tips
- Always observe only x-axis intersections.
- Touching the x-axis also counts as a zero.
- Count carefully from left to right.
- Practice graph observation questions regularly.
Practice MCQs
MCQ 1
A polynomial has 3 zeroes if its graph intersects the x-axis:
A. 1 time
B. 2 times
C. 3 times
D. 4 times
Answer:
C. 3 times
MCQ 2
The zeroes of a polynomial are the:
A. y-coordinates
B. x-coordinates
C. origin points
D. slopes
Answer:
B. x-coordinates
MCQ 3
A quadratic polynomial can have at most:
A. 1 zero
B. 2 zeroes
C. 3 zeroes
D. 4 zeroes
Answer:
B. 2 zeroes
MCQ 4
If the graph does not intersect the x-axis, then the polynomial has:
A. 1 zero
B. 2 zeroes
C. No zero
D. Infinite zeroes
Answer:
C. No zero
FAQ Section
What are zeroes of a polynomial?
The zeroes of a polynomial are the x-coordinates where the graph intersects the x-axis.
How many zeroes can a quadratic polynomial have?
A quadratic polynomial can have at most 2 zeroes.
Can a polynomial have no zeroes?
Yes, if its graph does not intersect the x-axis.
Why is Exercise 2.1 important?
It helps students understand graphical interpretation of polynomials which is important for board exams.
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