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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn graphical zeroes of cubic polynomials, x-axis intersections, degree of polynomials, and graph interpretation with detailed solutions and board 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:
Graphs provide a visual representation of polynomial behavior. By observing where a graph intersects the x-axis, students can determine the number of graphical zeroes of a polynomial. In this practice set, we focus on cubic polynomials and mixed graph-based concepts that are commonly tested in school and board examinations.
What You Will Learn?
✔ Graphical Zeroes of Cubic Polynomials
✔ x-axis Intersections
✔ Degree and Number of Zeroes
✔ Graph Interpretation
✔ Polynomial Analysis
✔ Board Exam Preparation
Why This Topic Is Important?
Graph-based questions strengthen conceptual understanding and help students connect algebraic formulas with visual representations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. A cubic polynomial can have at most:
A) $$1$$ zero
B) $$2$$ zeroes
C) $$3$$ zeroes
D) $$4$$ zeroes
Answer:
$$3$$
Useful Formula for this Question:
Maximum number of zeroes = Degree of polynomial.
Concept Behind This Question:
A cubic polynomial has degree:
$$3$$
Solution:
Degree:
$$3$$
Maximum possible zeroes:
$$3$$
Therefore, the correct answer is:
$$3$$
Exam Tip:
The maximum number of zeroes is always equal to the degree of the polynomial.
————————————————–
Q2. If the graph of a polynomial intersects the x-axis at three distinct points, the polynomial can be:
A) Linear
B) Quadratic
C) Cubic
D) Constant
Answer:
$$\text{Cubic}$$
Useful Formula for this Question:
Number of graphical zeroes = Number of x-axis intersections.
Concept Behind This Question:
Three distinct intersections indicate three graphical zeroes.
Solution:
Given:
The graph intersects the x-axis at:
$$3$$
distinct points.
Therefore:
Number of zeroes:
$$3$$
A polynomial with degree:
$$3$$
can have three zeroes.
Hence, the correct answer is:
$$\text{Cubic}$$
Exam Tip:
Count x-axis intersections carefully.
————————————————–
Q3. If a polynomial graph intersects the x-axis at:
$$x=-2,\ x=1,\ x=4$$
then the number of graphical zeroes is:
A) $$1$$
B) $$2$$
C) $$3$$
D) $$4$$
Answer:
$$3$$
Useful Formula for this Question:
Graphical zeroes = x-axis intersections.
Concept Behind This Question:
Each x-axis intersection represents one graphical zero.
Solution:
Given intersections:
$$x=-2$$
$$x=1$$
$$x=4$$
Total intersections:
$$3$$
Therefore:
Number of graphical zeroes:
$$3$$
Hence, the correct answer is:
$$3$$
Exam Tip:
Every distinct x-axis intersection corresponds to one zero.
————————————————–
Q4. Which of the following statements is correct?
A) Every polynomial has exactly one zero.
B) Every polynomial has exactly two zeroes.
C) Number of zeroes may vary depending on the polynomial.
D) Every polynomial has three zeroes.
Answer:
$$\text{Number of zeroes may vary depending on the polynomial}$$
Useful Formula for this Question:
Maximum number of zeroes = Degree.
Concept Behind This Question:
Different polynomials can have different numbers of zeroes.
Solution:
A linear polynomial can have:
$$1$$
zero.
A quadratic polynomial can have up to:
$$2$$
zeroes.
A cubic polynomial can have up to:
$$3$$
zeroes.
Therefore, the number of zeroes varies.
Hence, the correct answer is:
$$\text{Number of zeroes may vary depending on the polynomial}$$
Exam Tip:
Remember “maximum” does not mean “always equal to”.
————————————————–
Q5. The graph of a polynomial cuts the x-axis at exactly one point. The polynomial has:
A) $$0$$ graphical zeroes
B) $$1$$ graphical zero
C) $$2$$ graphical zeroes
D) Cannot be determined
Answer:
$$1$$
Useful Formula for this Question:
Graphical zeroes = x-axis intersections.
Concept Behind This Question:
One x-axis intersection means one graphical zero.
Solution:
Given:
The graph cuts the x-axis at:
$$1$$
point.
Therefore:
Number of graphical zeroes:
$$1$$
Hence, the correct answer is:
$$1$$
Exam Tip:
The words “cuts” and “intersects” both indicate an x-axis crossing.
————————————————–
Important Formulas and Concepts
Zero of Polynomial:
$$p(x)=0$$
Graphical Zero:
The x-coordinate where the graph intersects the x-axis.
Maximum Number of Zeroes:
$$\text{Degree of Polynomial}$$
Linear Polynomial:
Degree:
$$1$$
Maximum Zeroes:
$$1$$
Quadratic Polynomial:
Degree:
$$2$$
Maximum Zeroes:
$$2$$
Cubic Polynomial:
Degree:
$$3$$
Maximum Zeroes:
$$3$$
————————————————–
FAQs
Q. Can a cubic polynomial have fewer than three zeroes?
Answer:
Yes. A cubic polynomial can have one, two, or three graphical zeroes depending on its graph.
Q. What is a graphical zero?
Answer:
The x-coordinate where the graph intersects the x-axis.
Q. Why are graph-based questions important?
Answer:
They help students understand the visual meaning of polynomial zeroes.
————————————————–
Common Mistakes Students Make
❌ Confusing degree with the number of terms.
❌ Forgetting that the degree gives only the maximum number of zeroes.
❌ Counting turning points instead of x-axis intersections.
❌ Confusing x-axis and y-axis.
————————————————–
Quick Revision Notes
✔ Graphical zeroes are x-axis intersections.
✔ Maximum number of zeroes = Degree.
✔ Linear Polynomial → Maximum $$1$$ zero.
✔ Quadratic Polynomial → Maximum $$2$$ zeroes.
✔ Cubic Polynomial → Maximum $$3$$ zeroes.
✔ Count x-axis intersections to determine graphical zeroes.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students understand graphical zeroes of cubic polynomials and strengthen graph interpretation skills. Regular practice improves conceptual understanding and prepares students for board examination questions.
Related links
- Class 10 Maths Chapter 2 Polynomials (Graphical Zeroes)
- Class 10 Maths Chapter 2 Polynomials graphical representation of polynomials
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials )
- Class 10 Maths Chapter 2 Polynomials zeroes of polynomials
- Class 10 Maths Chapter 2 Polynomials formation
- Class 10 Maths Chapter 2 Forming Quadratic Polynomials
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
- Class10 Maths Chapter2 Polynomials (Zeroes of Polynomial) – Part 4
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