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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn graphical representation of polynomials, zeroes of polynomials, x-axis intersections, and board exam concepts with detailed solutions and exam tips.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
The graphical representation of polynomials is an important topic in Class 10 Mathematics. The zeroes of a polynomial can be identified from its graph by observing where the graph intersects the x-axis. Understanding this concept helps students connect algebra with coordinate geometry and improves conceptual understanding. This practice set focuses on graph-related MCQs commonly asked in school and board examinations.
What You Will Learn?
✔ Graphs of Polynomials
✔ Zeroes of Polynomials
✔ x-axis Intersections
✔ Relationship Between Graphs and Zeroes
✔ Coordinate Geometry Connections
✔ Board Exam Preparation
Why This Topic Is Important?
Graph-based questions test conceptual understanding and are frequently included in examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. The zeroes of a polynomial are represented graphically by the points where the graph intersects:
A) y-axis
B) x-axis
C) Origin only
D) Any point on the graph
Answer:
$$\text{x-axis}$$
Useful Formula for this Question:
A zero of a polynomial occurs where:
$$p(x)=0$$
Concept Behind This Question:
At the x-axis, the value of:
$$y=p(x)$$
becomes:
$$0$$
Solution:
A zero is the value of:
$$x$$
for which:
$$p(x)=0$$
On the graph, this happens where the curve meets the:
$$\text{x-axis}$$
Therefore, the correct answer is:
$$\text{x-axis}$$
Exam Tip:
Always remember: zeroes correspond to x-axis intersections.
————————————————–
Q2. A linear polynomial can have at most:
A) $$0$$ zeroes
B) $$1$$ zero
C) $$2$$ zeroes
D) $$3$$ zeroes
Answer:
$$1$$
Useful Formula for this Question:
Maximum number of zeroes = Degree of polynomial.
Concept Behind This Question:
A linear polynomial has degree:
$$1$$
Solution:
Degree:
$$1$$
Maximum number of zeroes:
$$1$$
Therefore, the correct answer is:
$$1$$
Exam Tip:
Degree and maximum number of zeroes are closely related.
————————————————–
Q3. A quadratic polynomial can have at most:
A) $$1$$ zero
B) $$2$$ zeroes
C) $$3$$ zeroes
D) $$4$$ zeroes
Answer:
$$2$$
Useful Formula for this Question:
Maximum number of zeroes = Degree of polynomial.
Concept Behind This Question:
A quadratic polynomial has degree:
$$2$$
Solution:
Degree:
$$2$$
Maximum number of zeroes:
$$2$$
Therefore, the correct answer is:
$$2$$
Exam Tip:
A quadratic graph can cut the x-axis at most two times.
————————————————–
Q4. If the graph of a polynomial intersects the x-axis at three distinct points, then the polynomial can be:
A) Linear
B) Constant
C) Cubic
D) Quadratic
Answer:
$$\text{Cubic}$$
Useful Formula for this Question:
Maximum number of zeroes = Degree.
Concept Behind This Question:
Three x-axis intersections indicate three zeroes.
Solution:
Number of x-axis intersections:
$$3$$
Therefore, the polynomial must have degree at least:
$$3$$
Hence, it can be a:
$$\text{Cubic Polynomial}$$
Therefore, the correct answer is:
$$\text{Cubic}$$
Exam Tip:
Count the x-axis intersections to estimate the degree.
————————————————–
Q5. The graph of:
$$y=p(x)$$
touches the x-axis at exactly two points. The polynomial has:
A) $$0$$ zeroes
B) $$1$$ zero
C) $$2$$ zeroes
D) $$3$$ zeroes
Answer:
$$2$$
Useful Formula for this Question:
Each x-axis intersection represents a zero.
Concept Behind This Question:
The number of x-axis intersections equals the number of graphical zeroes.
Solution:
Given:
The graph touches the x-axis at:
$$2$$
points.
Therefore, the polynomial has:
$$2$$
zeroes.
Hence, the correct answer is:
$$2$$
Exam Tip:
Each distinct x-axis contact point corresponds to a zero.
————————————————–
Important Formulas and Concepts
Zero of Polynomial:
$$p(x)=0$$
Graphical Meaning:
Zeroes are the x-coordinates of points where the graph intersects the x-axis.
Maximum Number of Zeroes:
$$\text{Degree of Polynomial}$$
Linear Polynomial:
Degree:
$$1$$
Quadratic Polynomial:
Degree:
$$2$$
Cubic Polynomial:
Degree:
$$3$$
————————————————–
FAQs
Q. How can we identify zeroes from a graph?
Answer:
By observing where the graph intersects the x-axis.
Q. Can a quadratic polynomial have three zeroes?
Answer:
No. A quadratic polynomial can have at most:
$$2$$
zeroes.
Q. What does the x-axis represent in polynomial graphs?
Answer:
Points where:
$$y=0$$
————————————————–
Common Mistakes Students Make
❌ Confusing x-axis with y-axis.
❌ Forgetting that zeroes occur when:
$$p(x)=0$$
❌ Counting turning points instead of x-axis intersections.
❌ Confusing degree with number of terms.
————————————————–
Quick Revision Notes
✔ Zeroes occur where:
$$p(x)=0$$
✔ Graphical zeroes are x-axis intersections.
✔ Linear Polynomial → Maximum $$1$$ zero
✔ Quadratic Polynomial → Maximum $$2$$ zeroes
✔ Cubic Polynomial → Maximum $$3$$ zeroes
✔ Maximum zeroes = Degree of polynomial
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students understand the graphical interpretation of polynomial zeroes and strengthen their conceptual understanding. Regular practice improves board exam performance and mathematical reasoning skills.
Related links
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials )
- Class 10 Maths Chapter 2 Polynomials zeroes of polynomials
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- Class10 Maths Chapter2 Polynomials MCQ – Part 7
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- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
- Class10 Maths Chapter2 Polynomials (Zeroes of Polynomial) – Part 4
- Class 10 Math Chapter 2 Polynomials (Zeroes of Polynomial) – Part 3
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