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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn zeroes of a polynomial, polynomial evaluation, verification of zeroes, and factor form 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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
The concept of zeroes of a polynomial is one of the most important topics in Class 10 Mathematics. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero. Understanding zeroes helps students solve equations, factorize polynomials, and interpret graphs. Board examinations frequently include questions based on finding and verifying zeroes. This practice set contains fresh questions designed to strengthen conceptual understanding and improve problem-solving skills.
What You Will Learn?
✔ Finding Zeroes of a Polynomial
✔ Verifying Zeroes
✔ Polynomial Evaluation
✔ Factor Form and Zeroes
✔ Board Exam Oriented Questions
✔ Algebraic Thinking Skills
Why This Topic Is Important?
Zeroes of polynomials form the basis of factorization and graph interpretation. A strong understanding of this topic helps students solve more advanced algebraic problems in later chapters.
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 zero of the polynomial:
$$p(x)=x-12$$
is:
A) $$-12$$
B) $$0$$
C) $$12$$
D) $$1$$
Answer:
$$12$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
To find a zero of a linear polynomial, set the polynomial equal to zero and solve for $$x$$.
Solution:
Given:
$$p(x)=x-12$$
Put:
$$p(x)=0$$
$$x-12=0$$
$$x=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
For expressions of the form:
$$x-a$$
the zero is:
$$a$$
————————————————–
Q2. Which of the following is a zero of:
$$p(x)=3x-15$$
A) $$3$$
B) $$4$$
C) $$5$$
D) $$15$$
Answer:
$$5$$
Useful Formula for this Question:
A zero makes the polynomial equal to zero.
Concept Behind This Question:
Students should learn how coefficients affect the value of the zero.
Solution:
Given:
$$3x-15=0$$
$$3x=15$$
$$x=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Always divide both sides by the coefficient of $$x$$ after isolating the variable term.
————————————————–
Q3. If:
$$p(x)=x^2-16$$
then:
$$p(4)=$$
A) $$0$$
B) $$4$$
C) $$8$$
D) $$16$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the given value into the polynomial.
Concept Behind This Question:
If substitution gives zero, the number is a zero of the polynomial.
Solution:
Given:
$$p(x)=x^2-16$$
Substitute:
$$x=4$$
$$p(4)=4^2-16$$
$$=16-16$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Always calculate the exponent first before subtraction.
————————————————–
Q4. Which of the following is a zero of:
$$p(x)=x+9$$
A) $$9$$
B) $$-9$$
C) $$1$$
D) $$0$$
Answer:
$$-9$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students must carefully handle positive and negative signs.
Solution:
Given:
$$x+9=0$$
$$x=-9$$
Therefore, the correct answer is:
$$-9$$
Exam Tip:
For expressions of the form:
$$x+a$$
the zero is:
$$-a$$
————————————————–
Q5. If:
$$p(x)=2x+6$$
then:
$$p(-3)=$$
A) $$-6$$
B) $$0$$
C) $$3$$
D) $$6$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the value directly into the polynomial.
Concept Behind This Question:
Polynomial evaluation is used to verify zeroes.
Solution:
Given:
$$p(x)=2x+6$$
Substitute:
$$x=-3$$
$$p(-3)=2(-3)+6$$
$$=-6+6$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Whenever the result becomes zero, the substituted value is a zero of the polynomial.
————————————————–
Important Formulas and Concepts
A number is a zero of a polynomial if:
$$p(x)=0$$
For a linear polynomial:
$$ax+b$$
Zero:
$$x=-\frac{b}{a}$$
Verification Rule:
If:
$$p(a)=0$$
then:
$$a$$
is a zero of the polynomial.
————————————————–
FAQs
Q. What is a zero of a polynomial?
Answer:
A value of the variable that makes the polynomial equal to:
$$0$$
Q. How do we check whether a number is a zero?
Answer:
Substitute the value into the polynomial. If the result is:
$$0$$
then it is a zero.
Q. Can a quadratic polynomial have more than one zero?
Answer:
Yes. A quadratic polynomial can have up to two zeroes.
————————————————–
Common Mistakes Students Make
❌ Sign mistakes while solving equations.
❌ Forgetting to substitute correctly.
❌ Assuming a value is a zero without verification.
❌ Ignoring brackets when substituting negative numbers.
————————————————–
Quick Revision Notes
✔ A zero makes the polynomial equal to:
$$0$$
✔ Verify using substitution.
✔ If:
$$p(a)=0$$
then:
$$a$$
is a zero.
✔ Linear polynomial:
$$ax+b$$
has one zero.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students understand how to find and verify the zeroes of a polynomial. Regular practice of such questions improves conceptual understanding and prepares students for board examinations and higher algebraic topics.
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