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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 coefficient relationships 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 zeroes and coefficients is a powerful tool in algebra. Instead of finding the actual zeroes, students can directly calculate their sum and product using simple formulas. This concept is frequently tested in board examinations and helps students solve polynomial questions more efficiently. In this practice set, students will apply these formulas to a variety of fresh NCERT-based questions.
What You Will Learn?
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Quadratic Polynomial Analysis
✔ Formula-Based Problem Solving
✔ Coefficient Identification
✔ Board Exam Preparation
Why This Topic Is Important?
Understanding these formulas saves time in examinations and builds a strong foundation for factorization and higher algebraic concepts.
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:
$$3x^2-12x+5$$
is:
A) $$4$$
B) $$-4$$
C) $$5$$
D) $$-5$$
Answer:
$$4$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The sum depends only on the coefficients of $$x^2$$ and $$x$$.
Solution:
Given:
$$a=3,\ b=-12$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-12}{3}$$
$$=\frac{12}{3}$$
$$=4$$
Therefore, the correct answer is:
$$4$$
Exam Tip:
Check the sign of $$b$$ carefully before substitution.
————————————————–
Q2. The product of zeroes of:
$$3x^2-12x+5$$
is:
A) $$\frac{5}{3}$$
B) $$-\frac{5}{3}$$
C) $$5$$
D) $$3$$
Answer:
$$\frac{5}{3}$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The product depends only on the leading coefficient and constant term.
Solution:
Given:
$$a=3,\ c=5$$
Using:
$$\frac{c}{a}$$
$$=\frac{5}{3}$$
Therefore, the correct answer is:
$$\frac{5}{3}$$
Exam Tip:
Always express the answer in its simplest fractional form.
————————————————–
Q3. For the polynomial:
$$2x^2+x-6$$
the sum of zeroes is:
A) $$-\frac{1}{2}$$
B) $$\frac{1}{2}$$
C) $$-1$$
D) $$1$$
Answer:
$$-\frac{1}{2}$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Even when coefficients are small, careful substitution is important.
Solution:
Given:
$$a=2,\ b=1$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{1}{2}$$
Therefore, the correct answer is:
$$-\frac{1}{2}$$
Exam Tip:
Do not forget the negative sign in the formula.
————————————————–
Q4. For the polynomial:
$$2x^2+x-6$$
the product of zeroes is:
A) $$3$$
B) $$-3$$
C) $$6$$
D) $$-6$$
Answer:
$$-3$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The sign of the constant term affects the sign of the product.
Solution:
Given:
$$a=2,\ c=-6$$
Using:
$$\frac{c}{a}$$
$$=\frac{-6}{2}$$
$$=-3$$
Therefore, the correct answer is:
$$-3$$
Exam Tip:
If $$c$$ is negative and $$a$$ is positive, the product will be negative.
————————————————–
Q5. If the sum of zeroes of a quadratic polynomial is:
$$5$$
and:
$$a=1$$
then the coefficient of $$x$$ is:
A) $$5$$
B) $$-5$$
C) $$1$$
D) $$-1$$
Answer:
$$-5$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Sometimes board questions ask students to find a coefficient using the formula in reverse.
Solution:
Given:
Sum of zeroes:
$$5$$
and:
$$a=1$$
Using:
$$-\frac{b}{a}=5$$
$$-\frac{b}{1}=5$$
$$-b=5$$
$$b=-5$$
Therefore, the coefficient of $$x$$ is:
$$-5$$
Hence, the correct answer is:
$$-5$$
Exam Tip:
Learn to apply the formulas in both directions—forward and reverse.
————————————————–
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 we find coefficients if the sum or product of zeroes is given?
Answer: Yes. The formulas can be used in reverse to determine unknown coefficients.
Q. Is it necessary to find actual zeroes first?
Answer: No. The formulas provide the sum and product directly.
Q. Why are these formulas important?
Answer: They save time and are frequently used in board examinations.
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in:
$$-\frac{b}{a}$$
❌ Using the wrong coefficient for substitution.
❌ Not simplifying fractions completely.
❌ Confusing sum and product formulas.
————————————————–
Quick Revision Notes
✔ For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ The coefficient of $$x$$ is represented by:
$$b$$
✔ These formulas can be used in reverse to find unknown coefficients.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students master the relationship between zeroes and coefficients of quadratic polynomials. Regular practice improves speed, accuracy, and confidence for board examinations.
Related links
- Class10 Maths Chapter2 Polynomials (Zeroes of Polynomial) – Part 4
- 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
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