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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn zeroes of polynomials, factor theorem basics, 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:
The concept of zeroes of a polynomial is essential for understanding factorization and algebraic equations. A zero of a polynomial is a value that makes the polynomial equal to zero. Students are often asked to identify zeroes, verify them through substitution, and understand their relationship with factors. This practice set includes fresh board-oriented questions that strengthen these concepts and improve problem-solving skills.
What You Will Learn?
✔ Finding Zeroes of Polynomials
✔ Verifying Zeroes
✔ Factor-Zero Relationship
✔ Polynomial Evaluation
✔ Algebraic Reasoning
✔ Board Exam Preparation
Why This Topic Is Important?
Zeroes of polynomials are used in factorization, graph interpretation, and solving equations. They form the foundation for many advanced algebraic concepts.
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:
$$p(x)=x-15$$
A) $$15$$
B) $$-15$$
C) $$5$$
D) $$0$$
Answer:
$$15$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
To find a zero of a linear polynomial, solve the equation obtained by setting the polynomial equal to zero.
Solution:
Given:
$$p(x)=x-15$$
Put:
$$p(x)=0$$
$$x-15=0$$
$$x=15$$
Therefore, the correct answer is:
$$15$$
Exam Tip:
For:
$$x-a$$
the zero is always:
$$a$$
————————————————–
Q2. If:
$$p(x)=x^2-49$$
then:
$$p(7)=$$
A) $$49$$
B) $$14$$
C) $$0$$
D) $$7$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the value directly into the polynomial.
Concept Behind This Question:
A value is a zero if substitution makes the polynomial equal to zero.
Solution:
Given:
$$p(x)=x^2-49$$
Substitute:
$$x=7$$
$$p(7)=7^2-49$$
$$=49-49$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
When the answer becomes zero after substitution, the number is a zero of the polynomial.
————————————————–
Q3. Which of the following is a factor corresponding to the zero:
$$4$$
A) $$x+4$$
B) $$x-4$$
C) $$4x-1$$
D) $$x+1$$
Answer:
$$x-4$$
Useful Formula for this Question:
If:
$$a$$
is a zero, then:
$$(x-a)$$
is a factor.
Concept Behind This Question:
Every zero of a polynomial has a corresponding linear factor.
Solution:
Given:
Zero:
$$4$$
Corresponding factor:
$$(x-4)$$
Therefore, the correct answer is:
$$x-4$$
Exam Tip:
Positive zero → factor has a negative sign.
Negative zero → factor has a positive sign.
————————————————–
Q4. Which of the following is a zero of:
$$p(x)=5x-25$$
A) $$25$$
B) $$10$$
C) $$5$$
D) $$-5$$
Answer:
$$5$$
Useful Formula for this Question:
For:
$$ax+b=0$$
Zero:
$$x=-\frac{b}{a}$$
Concept Behind This Question:
Linear polynomials have exactly one zero.
Solution:
Given:
$$5x-25=0$$
$$5x=25$$
$$x=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Divide both sides by the coefficient of $$x$$ after isolating the variable term.
————————————————–
Q5. If:
$$p(x)=x^2-64$$
then:
$$p(-8)=$$
A) $$0$$
B) $$8$$
C) $$64$$
D) $$-64$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the given value into the polynomial.
Concept Behind This Question:
A polynomial can have positive and negative zeroes.
Solution:
Given:
$$p(x)=x^2-64$$
Substitute:
$$x=-8$$
$$p(-8)=(-8)^2-64$$
$$=64-64$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Always use brackets when 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.
————————————————–
FAQs
Q. What is the relationship between a factor and a zero?
Answer:
If:
$$a$$
is a zero of a polynomial, then:
$$(x-a)$$
is a factor of that polynomial.
Q. Can a polynomial have more than one zero?
Answer:
Yes. Depending on its degree, a polynomial may have multiple zeroes.
Q. Why do we substitute values into a polynomial?
Answer:
Substitution helps verify whether a given number is a zero.
————————————————–
Common Mistakes Students Make
❌ Sign errors while finding zeroes.
❌ Forgetting brackets with negative numbers.
❌ Confusing factors with zeroes.
❌ Calculation mistakes during substitution.
————————————————–
Quick Revision Notes
✔ A zero makes the polynomial equal to:
$$0$$
✔ Verify zeroes using substitution.
✔ For:
$$ax+b$$
Zero:
$$x=-\frac{b}{a}$$
✔ If $$a$$ is a zero, then:
$$(x-a)$$
is a factor.
✔ Positive and negative values can both be zeroes.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs strengthen students’ understanding of zeroes, factors, and polynomial evaluation. Regular practice of such questions improves conceptual clarity and prepares students for board examinations and advanced algebraic topics.
Related links
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