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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn zeroes of a polynomial, finding zeroes, verification of zeroes, and polynomial evaluation with detailed solutions and exam tips for CBSE board exams.
Do You Know
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
After learning the basics of polynomials, the next important concept is the zeroes of a polynomial. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero. This concept is extremely important because it forms the foundation for factorization, graphing, and solving polynomial equations. In board examinations, students are often asked to identify or verify the zeroes of a given polynomial. This practice set introduces the concept through carefully selected MCQs with step-by-step solutions and exam tips.
What You Will Learn?
✔ Meaning of Zeroes of a Polynomial
✔ Finding Zeroes
✔ Verification of Zeroes
✔ Polynomial Evaluation
✔ Relationship Between Polynomial and Its Zeroes
✔ Board Exam Oriented Questions
Why This Topic Is Important?
Zeroes of polynomials help students understand how polynomial equations behave. This concept is frequently used in factorization, graph-based questions, and higher algebra.
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:
$$p(x)=x-5$$
is:
A) $$-5$$
B) $$0$$
C) $$5$$
D) $$1$$
Answer:
$$5$$
Useful Formula for this Question:
A zero of a polynomial satisfies:
$$p(x)=0$$
Concept Behind This Question:
To find a zero, substitute values that make the polynomial equal to zero.
Solution:
Given:
$$p(x)=x-5$$
Put:
$$p(x)=0$$
Therefore:
$$x-5=0$$
$$x=5$$
Hence, the correct answer is:
$$5$$
Exam Tip:
For linear polynomials, simply solve:
$$p(x)=0$$
————————————————–
Q2. Which of the following is a zero of:
$$p(x)=x+7$$
A) $$7$$
B) $$-7$$
C) $$0$$
D) $$1$$
Answer:
$$-7$$
Useful Formula for this Question:
A zero makes the polynomial equal to zero.
Concept Behind This Question:
Students must understand that the zero is not always the same sign as the constant term.
Solution:
Given:
$$p(x)=x+7$$
Put:
$$p(x)=0$$
$$x+7=0$$
$$x=-7$$
Therefore, the correct answer is:
$$-7$$
Exam Tip:
Always move the constant term to the other side carefully and check the sign.
————————————————–
Q3. If:
$$p(x)=x^2-9$$
then:
$$p(3)=$$
A) $$0$$
B) $$3$$
C) $$6$$
D) $$9$$
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 makes the polynomial equal to zero.
Solution:
Given:
$$p(x)=x^2-9$$
Substitute:
$$x=3$$
$$p(3)=3^2-9$$
$$=9-9$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Whenever the result is zero, the substituted value is a zero of the polynomial.
————————————————–
Q4. Which of the following is a zero of:
$$p(x)=2x-8$$
A) $$2$$
B) $$3$$
C) $$4$$
D) $$8$$
Answer:
$$4$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students should learn to solve simple linear polynomial equations.
Solution:
Given:
$$p(x)=2x-8$$
Put:
$$2x-8=0$$
$$2x=8$$
$$x=4$$
Therefore, the correct answer is:
$$4$$
Exam Tip:
First isolate the variable term, then divide by its coefficient.
————————————————–
Q5. If:
$$p(x)=x^2-4$$
then:
$$p(2)=$$
A) $$0$$
B) $$2$$
C) $$4$$
D) $$8$$
Answer:
$$0$$
Useful Formula for this Question:
Substitute the value of $$x$$ into the polynomial.
Concept Behind This Question:
Polynomial evaluation helps verify whether a number is a zero.
Solution:
Given:
$$p(x)=x^2-4$$
Substitute:
$$x=2$$
$$p(2)=2^2-4$$
$$=4-4$$
$$=0$$
Therefore, the correct answer is:
$$0$$
Exam Tip:
Board exams often ask students to verify whether a given number is a zero of a polynomial.
————————————————–
Important Formulas and Concepts
A number is a zero of a polynomial if:
$$p(x)=0$$
For a linear polynomial:
$$ax+b$$
Zero:
$$x=-\frac{b}{a}$$
To verify a zero:
Substitute the value into the polynomial.
If the result is:
$$0$$
then it is a zero.
————————————————–
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 verify a zero?
Answer:
Substitute the value into the polynomial and check whether the result is:
$$0$$
Q. Can a polynomial have more than one zero?
Answer:
Yes. Depending on its degree, a polynomial can have multiple zeroes.
————————————————–
Common Mistakes Students Make
❌ Forgetting to substitute correctly.
❌ Making sign errors while solving equations.
❌ Assuming every given number is a zero.
❌ Not checking whether the polynomial becomes zero.
————————————————–
Quick Revision Notes
✔ A zero makes the polynomial equal to:
$$0$$
✔ Verify by substitution.
✔ If:
$$p(a)=0$$
then:
$$a$$
is a zero of the polynomial.
✔ Linear polynomial:
$$ax+b$$
has one zero.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs introduce the concept of zeroes of a polynomial through simple and exam-oriented questions. Mastering this topic is essential for understanding factorization, polynomial graphs, and higher algebraic concepts.
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