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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn graphical zeroes of linear and quadratic polynomials, x-axis intersections, degree and number of zeroes 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 method for understanding polynomial zeroes. The points where a polynomial graph cuts or touches the x-axis represent its zeroes. In this practice set, students will strengthen their understanding of graphical zeroes, degree of polynomials, and the relationship between graphs and algebraic expressions. These concepts are important for school examinations and board-level problem-solving.
What You Will Learn?
✔ Graphical Zeroes
✔ Linear Polynomial Graphs
✔ Quadratic Polynomial Graphs
✔ x-axis Intersections
✔ Degree and Number of Zeroes
✔ Board Exam Preparation
Why This Topic Is Important?
Graphical questions help students connect algebraic concepts with visual interpretation, making polynomial concepts easier to understand.
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 graph of a linear polynomial intersects the x-axis at:
A) At most $$1$$ point
B) At most $$2$$ points
C) At most $$3$$ points
D) Infinite points
Answer:
$$1$$ point
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:
$$1$$
Hence, the graph can intersect the x-axis at only:
$$1$$
point.
Therefore, the correct answer is:
$$1$$ point.
Exam Tip:
A straight line can cross the x-axis only once.
————————————————–
Q2. The graph of a quadratic polynomial can intersect the x-axis at:
A) At most $$1$$ point
B) At most $$2$$ points
C) At most $$3$$ points
D) Infinite points
Answer:
$$2$$ points
Useful Formula for this Question:
Maximum number of zeroes = Degree.
Concept Behind This Question:
A quadratic polynomial has degree:
$$2$$
Solution:
Degree:
$$2$$
Maximum possible zeroes:
$$2$$
Therefore, the graph can intersect the x-axis at:
$$2$$
points.
Hence, the correct answer is:
$$2$$ points.
Exam Tip:
A parabola may cut the x-axis twice, once, or not at all.
————————————————–
Q3. If a polynomial graph does not intersect the x-axis, then the number of graphical zeroes is:
A) $$0$$
B) $$1$$
C) $$2$$
D) $$3$$
Answer:
$$0$$
Useful Formula for this Question:
Graphical zeroes = x-axis intersections.
Concept Behind This Question:
Without intersection, there are no graphical zeroes.
Solution:
Given:
No x-axis intersection.
Therefore:
Number of graphical zeroes:
$$0$$
Hence, the correct answer is:
$$0$$
Exam Tip:
No intersection means no graphical zeroes.
————————————————–
Q4. If the graph of a quadratic polynomial touches the x-axis at exactly one point, then the number of graphical zeroes is:
A) $$0$$
B) $$1$$
C) $$2$$
D) $$3$$
Answer:
$$1$$
Useful Formula for this Question:
Every distinct x-axis contact point represents a graphical zero.
Concept Behind This Question:
Touching the x-axis at one point gives one graphical zero.
Solution:
Given:
Graph touches the x-axis at exactly:
$$1$$
point.
Therefore:
Number of graphical zeroes:
$$1$$
Hence, the correct answer is:
$$1$$
Exam Tip:
Touching and crossing both count as x-axis contacts.
————————————————–
Q5. A polynomial graph intersects the x-axis at two distinct points. The polynomial can be:
A) Constant Polynomial
B) Linear Polynomial
C) Quadratic Polynomial
D) Zero Polynomial
Answer:
$$\text{Quadratic Polynomial}$$
Useful Formula for this Question:
Maximum number of zeroes = Degree.
Concept Behind This Question:
Two distinct x-axis intersections indicate two zeroes.
Solution:
Number of graphical zeroes:
$$2$$
A polynomial with degree:
$$2$$
can have two zeroes.
Therefore, the polynomial can be:
$$\text{Quadratic Polynomial}$$
Hence, the correct answer is:
$$\text{Quadratic Polynomial}$$
Exam Tip:
Two distinct x-axis intersections usually indicate a quadratic graph.
————————————————–
Important Formulas and Concepts
Zero of Polynomial:
$$p(x)=0$$
Graphical Zero:
The x-coordinate of a point 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:
$$2$$
————————————————–
FAQs
Q. What is a graphical zero?
Answer:
The x-coordinate where the graph intersects the x-axis.
Q. Can a quadratic polynomial have only one graphical zero?
Answer:
Yes. If the graph touches the x-axis at exactly one point.
Q. What happens if a graph never touches the x-axis?
Answer:
The polynomial has:
$$0$$
graphical zeroes.
————————————————–
Common Mistakes Students Make
❌ Counting turning points instead of x-axis intersections.
❌ Confusing x-axis and y-axis.
❌ Assuming every quadratic graph must have two zeroes.
❌ Ignoring points where the graph only touches the x-axis.
————————————————–
Quick Revision Notes
✔ Graphical zeroes are x-axis intersections.
✔ Linear Polynomial → Maximum $$1$$ zero.
✔ Quadratic Polynomial → Maximum $$2$$ zeroes.
✔ No x-axis intersection → $$0$$ graphical zeroes.
✔ One x-axis touch → $$1$$ graphical zero.
✔ Two x-axis intersections → $$2$$ graphical zeroes.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students understand graphical zeroes of linear and quadratic polynomials. Regular practice strengthens conceptual understanding and improves performance in board examinations
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