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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Solve higher-order thinking questions on zeroes of polynomials, sum and product of zeroes, and polynomial formation with detailed solutions and exam tips.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Advanced Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
After mastering the basic formulas of Chapter 2, students should practice higher-order thinking questions (HOTS). These questions require deeper understanding of the relationship between zeroes and coefficients and often appear in board exams, Olympiad-level school tests, and scholarship examinations. This set focuses on concept application rather than direct formula substitution.
What You Will Learn?
✔ Higher Order Thinking Questions (HOTS)
✔ Relationship Between Zeroes and Coefficients
✔ Reverse Formula Applications
✔ Polynomial Formation
✔ Logical Reasoning in Algebra
✔ Board Exam Preparation
Why This Topic Is Important?
Advanced questions improve conceptual clarity and prepare students for difficult examination questions.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
✔ NTSE-Level Practice
Q1. If the zeroes of a quadratic polynomial are:
$$-3,\ 8$$
then the sum of the zeroes is:
A) $$11$$
B) $$5$$
C) $$-5$$
D) $$-11$$
Answer:
$$5$$
Useful Formula for this Question:
Sum of zeroes:
$$\alpha+\beta$$
Concept Behind This Question:
The sum can be found directly from the given zeroes.
Solution:
Given zeroes:
$$-3,\ 8$$
Sum:
$$-3+8$$
$$=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Pay special attention to negative numbers while adding.
————————————————–
Q2. If the zeroes of a quadratic polynomial are:
$$-3,\ 8$$
then the product of the zeroes is:
A) $$24$$
B) $$-24$$
C) $$11$$
D) $$-11$$
Answer:
$$-24$$
Useful Formula for this Question:
Product of zeroes:
$$\alpha\beta$$
Concept Behind This Question:
The sign of the product depends on the signs of the zeroes.
Solution:
Given:
$$-3,\ 8$$
Product:
$$(-3)\times8$$
$$=-24$$
Therefore, the correct answer is:
$$-24$$
Exam Tip:
A positive number multiplied by a negative number gives a negative result.
————————————————–
Q3. The quadratic polynomial whose zeroes are:
$$-3,\ 8$$
is:
A) $$x^2-5x-24$$
B) $$x^2+5x-24$$
C) $$x^2-5x+24$$
D) $$x^2+5x+24$$
Answer:
$$x^2-5x-24$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Concept Behind This Question:
A polynomial can be formed using the sum and product of its zeroes.
Solution:
Sum:
$$5$$
Product:
$$-24$$
Using:
$$x^2-(5)x+(-24)$$
$$x^2-5x-24$$
Therefore, the correct answer is:
$$x^2-5x-24$$
Exam Tip:
Substitute the sum and product carefully with correct signs.
————————————————–
Q4. If the sum of zeroes of:
$$5x^2+kx+9$$
is:
$$-4$$
then the value of:
$$k$$
is:
A) $$20$$
B) $$-20$$
C) $$4$$
D) $$-4$$
Answer:
$$20$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The coefficient can be found using reverse application of the formula.
Solution:
Given:
$$a=5$$
and:
$$-\frac{k}{5}=-4$$
Multiplying both sides by:
$$5$$
$$-k=-20$$
$$k=20$$
Therefore, the correct answer is:
$$20$$
Exam Tip:
Reverse-formula questions are very common in board examinations.
————————————————–
Q5. If the product of zeroes of:
$$7x^2-3x+k$$
is:
$$2$$
then the value of:
$$k$$
is:
A) $$14$$
B) $$-14$$
C) $$7$$
D) $$2$$
Answer:
$$14$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The constant term can be determined directly using the product formula.
Solution:
Given:
$$\frac{k}{7}=2$$
Multiplying both sides by:
$$7$$
$$k=14$$
Therefore, the correct answer is:
$$14$$
Exam Tip:
For product questions, only $$a$$ and $$c$$ are required.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
For zeroes:
$$\alpha,\ \beta$$
Quadratic Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Reverse Formula:
$$b=-a \times (\text{sum of zeroes})$$
$$c=a \times (\text{product of zeroes})$$
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FAQs
Q. What are HOTS questions?
Answer:
Higher Order Thinking Questions test understanding, reasoning, and application of concepts rather than direct memorization.
Q. Are such questions asked in board exams?
Answer:
Yes. Many board questions require concept application similar to HOTS problems.
Q. How can students improve in such questions?
Answer:
Practice mixed and reverse-formula questions regularly.
————————————————–
Common Mistakes Students Make
❌ Sign errors while finding the sum.
❌ Sign errors while finding the product.
❌ Incorrect substitution in formulas.
❌ Forgetting to simplify the final answer.
————————————————–
Quick Revision Notes
✔ Sum of zeroes:
$$\alpha+\beta$$
or
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\alpha\beta$$
or
$$\frac{c}{a}$$
✔ Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
✔ Reverse formulas are frequently used in exams.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students strengthen higher-order thinking skills and master advanced applications of the relationship between zeroes and coefficients. Regular practice improves confidence and examination performance.
Related links
- Class 10 Maths Chapter 2 Polynomials formation
- Class 10 Maths Chapter 2 Forming Quadratic Polynomials
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
- Class10 Maths Chapter2 Polynomials (Zeroes of Polynomial) – Part 4
- Class 10 Math Chapter 2 Polynomials (Zeroes of Polynomial) – Part 3
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