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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn how to form quadratic polynomials from given zeroes, sum and product of zeroes, and relationship between zeroes and coefficients 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: Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
One of the most important applications of the relationship between zeroes and coefficients is forming a quadratic polynomial when the zeroes are given. Instead of factorization, students can use the sum and product of zeroes to directly construct the required polynomial. This concept is frequently asked in CBSE and State Board examinations. This practice set focuses on developing this skill through board-level MCQs and detailed solutions.
What You Will Learn?
✔ Forming Quadratic Polynomials
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Relationship Between Zeroes and Coefficients
✔ Polynomial Construction
✔ Board Exam Preparation
Why This Topic Is Important?
Questions based on forming polynomials are common in examinations and help students connect different concepts within the chapter.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. If the zeroes of a quadratic polynomial are:
$$2,\ 5$$
then the polynomial is:
A) $$x^2-7x+10$$
B) $$x^2+7x+10$$
C) $$x^2-10x+7$$
D) $$x^2+10x+7$$
Answer:
$$x^2-7x+10$$
Useful Formula for this Question:
For zeroes:
$$\alpha,\ \beta$$
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Concept Behind This Question:
A quadratic polynomial can be formed directly using the sum and product of its zeroes.
Solution:
Given zeroes:
$$2,\ 5$$
Sum:
$$2+5=7$$
Product:
$$2\times5=10$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
$$x^2-7x+10$$
Therefore, the correct answer is:
$$x^2-7x+10$$
Exam Tip:
Always calculate the sum and product before forming the polynomial.
————————————————–
Q2. If the zeroes of a quadratic polynomial are:
$$3,\ 4$$
then the sum of zeroes is:
A) $$7$$
B) $$12$$
C) $$1$$
D) $$-7$$
Answer:
$$7$$
Useful Formula for this Question:
Sum of zeroes:
$$\alpha+\beta$$
Concept Behind This Question:
The sum is obtained by adding both zeroes.
Solution:
Given zeroes:
$$3,\ 4$$
Sum:
$$3+4=7$$
Therefore, the correct answer is:
$$7$$
Exam Tip:
Do not confuse sum with product.
————————————————–
Q3. If the zeroes of a quadratic polynomial are:
$$3,\ 4$$
then the product of zeroes is:
A) $$7$$
B) $$12$$
C) $$1$$
D) $$-12$$
Answer:
$$12$$
Useful Formula for this Question:
Product of zeroes:
$$\alpha\beta$$
Concept Behind This Question:
The product is obtained by multiplying both zeroes.
Solution:
Given zeroes:
$$3,\ 4$$
Product:
$$3\times4=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Multiply carefully and check signs if negative numbers are involved.
————————————————–
Q4. If the zeroes are:
$$-2,\ 3$$
then the quadratic polynomial is:
A) $$x^2-x-6$$
B) $$x^2+x-6$$
C) $$x^2-x+6$$
D) $$x^2+x+6$$
Answer:
$$x^2-x-6$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Concept Behind This Question:
Negative zeroes affect both the sum and product.
Solution:
Given zeroes:
$$-2,\ 3$$
Sum:
$$-2+3=1$$
Product:
$$-2\times3=-6$$
Using:
$$x^2-(1)x+(-6)$$
$$x^2-x-6$$
Therefore, the correct answer is:
$$x^2-x-6$$
Exam Tip:
Check the signs carefully when one zero is negative.
————————————————–
Q5. If the sum of zeroes is:
$$8$$
and the product of zeroes is:
$$15$$
then the quadratic polynomial is:
A) $$x^2-8x+15$$
B) $$x^2+8x+15$$
C) $$x^2-15x+8$$
D) $$x^2+15x+8$$
Answer:
$$x^2-8x+15$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\text{sum})x+(\text{product})$$
Concept Behind This Question:
A quadratic polynomial can be formed directly if the sum and product are known.
Solution:
Given:
Sum:
$$8$$
Product:
$$15$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
$$x^2-8x+15$$
Therefore, the correct answer is:
$$x^2-8x+15$$
Exam Tip:
This is one of the most frequently asked board exam question types.
————————————————–
Important Formulas and Concepts
For zeroes:
$$\alpha,\ \beta$$
Sum of zeroes:
$$\alpha+\beta$$
Product of zeroes:
$$\alpha\beta$$
Quadratic Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Alternative Form:
$$x^2-(\text{sum of zeroes})x+(\text{product of zeroes})$$
————————————————–
FAQs
Q. Can we form a polynomial if only the zeroes are given?
Answer:
Yes. First find the sum and product of the zeroes, then apply the formula.
Q. Can negative zeroes be used?
Answer:
Yes. Sign calculations must be done carefully.
Q. Is this topic important for board exams?
Answer:
Yes. Questions based on forming polynomials are very common.
————————————————–
Common Mistakes Students Make
❌ Confusing sum and product.
❌ Sign mistakes with negative zeroes.
❌ Writing the wrong sign before the middle term.
❌ Forgetting to simplify before forming the polynomial.
————————————————–
Quick Revision Notes
✔ Sum of zeroes:
$$\alpha+\beta$$
✔ Product of zeroes:
$$\alpha\beta$$
✔ Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
✔ Check signs carefully.
✔ Practice both positive and negative zeroes.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students master the process of forming quadratic polynomials from given zeroes. Regular practice improves conceptual understanding and prepares students for board examination questions.
Related links
- 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
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- Class 10 Maths Chapter 2 Polynomials MCQ (Zeroes of a Polynomial) part 2
- Class 10 Maths Chapter 2 Polynomials (Zeroes of a Polynomial) – Part 1
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