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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn sum of zeroes, product of zeroes, quadratic polynomials, and relationship between zeroes and coefficients 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 relationship between the zeroes and coefficients of a quadratic polynomial is one of the most important concepts in algebra. Using simple formulas, students can determine the sum and product of zeroes without actually calculating the zeroes themselves. This concept saves time in examinations and helps students solve higher-level polynomial problems efficiently. This practice set contains fresh board-oriented questions that focus on applying these formulas in different situations.
What You Will Learn?
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Coefficient-Based Questions
✔ Quadratic Polynomials
✔ Formula Applications
✔ Board Exam Preparation
Why This Topic Is Important?
Questions based on the relationship between zeroes and coefficients are regularly asked in board examinations. A strong understanding of these formulas improves speed and accuracy.
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 sum of zeroes of:
$$2x^2-8x+3$$
is:
A) $$4$$
B) $$-4$$
C) $$3$$
D) $$-3$$
Answer:
$$4$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The sum of zeroes depends only on the coefficients $$a$$ and $$b$$.
Solution:
Given:
$$a=2,\ b=-8$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-8}{2}$$
$$=\frac{8}{2}$$
$$=4$$
Therefore, the correct answer is:
$$4$$
Exam Tip:
Always simplify the fraction completely before selecting the answer.
————————————————–
Q2. The product of zeroes of:
$$4x^2+7x-2$$
is:
A) $$-\frac{1}{2}$$
B) $$\frac{1}{2}$$
C) $$-2$$
D) $$2$$
Answer:
$$-\frac{1}{2}$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The product of zeroes depends on the constant term and leading coefficient.
Solution:
Given:
$$a=4,\ c=-2$$
Using:
$$\frac{c}{a}$$
$$=\frac{-2}{4}$$
$$=-\frac{1}{2}$$
Therefore, the correct answer is:
$$-\frac{1}{2}$$
Exam Tip:
Reduce fractions to their simplest form whenever possible.
————————————————–
Q3. If the quadratic polynomial is:
$$x^2-9x+20$$
then the sum of its zeroes is:
A) $$9$$
B) $$-9$$
C) $$20$$
D) $$-20$$
Answer:
$$9$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students should be able to identify coefficients correctly before applying formulas.
Solution:
Given:
$$a=1,\ b=-9$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-9}{1}$$
$$=9$$
Therefore, the correct answer is:
$$9$$
Exam Tip:
The coefficient of $$x^2$$ is always $$a$$ and the coefficient of $$x$$ is always $$b$$.
————————————————–
Q4. If the quadratic polynomial is:
$$x^2-9x+20$$
then the product of its zeroes is:
A) $$9$$
B) $$20$$
C) $$-9$$
D) $$-20$$
Answer:
$$20$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The constant term plays a direct role in determining the product of zeroes.
Solution:
Given:
$$a=1,\ c=20$$
Using:
$$\frac{c}{a}$$
$$=\frac{20}{1}$$
$$=20$$
Therefore, the correct answer is:
$$20$$
Exam Tip:
For many board questions, the product can be found in just one step using the formula.
————————————————–
Q5. For the polynomial:
$$5x^2+15x+10$$
the sum of zeroes is:
A) $$-3$$
B) $$3$$
C) $$2$$
D) $$-2$$
Answer:
$$-3$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students should learn to simplify the result after applying the formula.
Solution:
Given:
$$a=5,\ b=15$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{15}{5}$$
$$=-3$$
Therefore, the correct answer is:
$$-3$$
Exam Tip:
After substitution, always simplify the fraction to get the final answer.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
where:
$$a \ne 0$$
————————————————–
FAQs
Q. Can the sum of zeroes be negative?
Answer:
Yes. It depends on the values of $$a$$ and $$b$$.
Q. Can the product of zeroes be negative?
Answer:
Yes. If $$c$$ and $$a$$ have opposite signs, the product will be negative.
Q. Do we need to calculate actual zeroes to find their sum and product?
Answer:
No. The formulas provide the answer directly.
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in the sum formula.
❌ Using the coefficient of $$x$$ in the product formula.
❌ Incorrectly identifying $$a$$, $$b$$, and $$c$$.
❌ Not simplifying fractions completely.
————————————————–
Quick Revision Notes
✔ For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ Identify coefficients carefully.
✔ Simplify fractions before finalizing answers.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students strengthen their understanding of the relationship between zeroes and coefficients. Mastering these formulas improves speed, confidence, and performance in board examinations.
Related links
- Class 10 Math Chapter 2 Polynomials (Zeroes of Polynomial) – Part 3
- Class 10 Math Chapter 2 Polynomials (Zeroes of Polynomial) – Part 2
- 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
- Class 10 Maths Chapter 2 Polynomials verification
- Class 10 Maths Chapter 2 Polynomials identification
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