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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn zeroes of a polynomial, factor form, polynomial evaluation, and verification of zeroes with detailed solutions and exam tips for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction:
Zeroes of a polynomial play a crucial role in algebra and are widely used in factorization and graph-related concepts. A zero of a polynomial is a value that makes the polynomial equal to zero. Students often encounter questions where they need to identify, verify, or calculate the zeroes of a polynomial. This practice set focuses on strengthening these skills through fresh and exam-oriented MCQs with detailed explanations.
What You Will Learn?
✔ Finding Zeroes of a Polynomial
✔ Verification of Zeroes
✔ Polynomial Evaluation
✔ Factor Form of Polynomials
✔ Algebraic Reasoning
✔ Board Exam Preparation
Why This Topic Is Important?
Understanding zeroes helps students solve polynomial equations, factorize expressions, and interpret graphs. These concepts are frequently tested in school and board 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. Which of the following is a zero of:
$$p(x)=x-20$$
A) $$-20$$
B) $$20$$
C) $$10$$
D) $$0$$
Answer:
$$20$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
The value that makes the polynomial equal to zero is called its zero.
Solution:
Given:
$$p(x)=x-20$$
Put:
$$p(x)=0$$
$$x-20=0$$
$$x=20$$
Therefore, the correct answer is:
$$20$$
Exam Tip:
For expressions of the form:
$$x-a$$
the zero is always:
$$a$$
————————————————–
Q2. If:
$$p(x)=x^2-25$$
then:
$$p(5)=$$
A) $$25$$
B) $$10$$
C) $$5$$
D) $$0$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the given value into the polynomial.
Concept Behind This Question:
A value is a zero if substituting it gives zero.
Solution:
Given:
$$p(x)=x^2-25$$
Substitute:
$$x=5$$
$$p(5)=5^2-25$$
$$=25-25$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Whenever substitution results in zero, the number is a zero of the polynomial.
————————————————–
Q3. Which of the following is a factor of:
$$x-8$$
A) $$x+8$$
B) $$x-4$$
C) $$x-8$$
D) $$x+4$$
Answer:
$$x-8$$
Useful Formula for this Question:
If $$a$$ is a zero, then:
$$(x-a)$$
is a factor.
Concept Behind This Question:
The factor form directly reveals the zero of a polynomial.
Solution:
The polynomial itself is:
$$x-8$$
Therefore:
$$(x-8)$$
is its factor.
The corresponding zero is:
$$8$$
Hence, the correct answer is:
$$x-8$$
Exam Tip:
Remember:
Zero $$a$$ ↔ Factor $$(x-a)$$
————————————————–
Q4. Which of the following is a zero of:
$$p(x)=4x+12$$
A) $$-3$$
B) $$3$$
C) $$12$$
D) $$4$$
Answer:
$$-3$$
Useful Formula for this Question:
For:
$$ax+b=0$$
Zero:
$$x=-\frac{b}{a}$$
Concept Behind This Question:
Students should learn to solve linear polynomials efficiently.
Solution:
Given:
$$4x+12=0$$
$$4x=-12$$
$$x=-3$$
Therefore, the correct answer is:
$$-3$$
Exam Tip:
Always simplify completely before selecting the answer.
————————————————–
Q5. If:
$$p(x)=x^2-36$$
then:
$$p(-6)=$$
A) $$-36$$
B) $$6$$
C) $$0$$
D) $$36$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the given value into the polynomial.
Concept Behind This Question:
Negative values can also be zeroes of a polynomial.
Solution:
Given:
$$p(x)=x^2-36$$
Substitute:
$$x=-6$$
$$p(-6)=(-6)^2-36$$
$$=36-36$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Always use brackets while substituting negative values.
————————————————–
Important Formulas and Concepts
A number is a zero of a polynomial if:
$$p(x)=0$$
For a linear polynomial:
$$ax+b$$
Zero:
$$x=-\frac{b}{a}$$
Factor-Zero Relationship:
If:
$$a$$
is a zero, then:
$$(x-a)$$
is a factor.
Verification Rule:
If:
$$p(a)=0$$
then:
$$a$$
is a zero of the polynomial.
————————————————–
FAQs
Q. What is the connection between factors and zeroes?
Answer:
If $$a$$ is a zero of a polynomial, then:
$$(x-a)$$
is a factor of that polynomial.
Q. Can a negative number be a zero?
Answer:
Yes. Any real number can be a zero if it makes the polynomial equal to zero.
Q. How do we verify a zero?
Answer:
Substitute the value into the polynomial and check whether the result becomes:
$$0$$
————————————————–
Common Mistakes Students Make
❌ Ignoring negative signs.
❌ Forgetting brackets while substituting negative values.
❌ Confusing factors and zeroes.
❌ Making calculation mistakes during substitution.
————————————————–
Quick Revision Notes
✔ A zero makes the polynomial equal to:
$$0$$
✔ Verify by substitution.
✔ For:
$$ax+b$$
Zero:
$$x=-\frac{b}{a}$$
✔ If $$a$$ is a zero, then:
$$(x-a)$$
is a factor.
✔ Negative numbers can also be zeroes.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students strengthen their understanding of zeroes, factors, and polynomial evaluation. Regular practice improves algebraic skills and prepares students for board-level questions.
Related links
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