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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn the relationship between zeroes and coefficients of quadratic polynomials with detailed solutions, formulas, 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:
One of the most important concepts in Chapter 2 is the relationship between the zeroes and coefficients of a quadratic polynomial. Instead of finding the zeroes directly, students can use formulas to determine their sum and product. This concept is frequently asked in board examinations and forms the foundation for many higher-level algebraic topics. In this practice set, students will learn how to apply these formulas through carefully designed MCQs and step-by-step solutions.
What You Will Learn?
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Quadratic Polynomials
✔ Relationship Between Zeroes and Coefficients
✔ Formula-Based Questions
✔ Board Exam Preparation
Why This Topic Is Important?
The relationship between zeroes and coefficients helps students solve polynomial problems quickly without always calculating the actual zeroes. It is one of the most frequently tested concepts in board exams.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. For the quadratic polynomial:
$$x^2-7x+10$$
the sum of zeroes is:
A) $$7$$
B) $$-7$$
C) $$10$$
D) $$-10$$
Answer:
$$7$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The sum of zeroes can be found directly from the coefficients without finding the actual zeroes.
Solution:
Given:
$$a=1,\ b=-7$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-7}{1}$$
$$=7$$
Therefore, the correct answer is:
$$7$$
Exam Tip:
For the sum of zeroes, always focus on the coefficient of $$x$$.
————————————————–
Q2. For the quadratic polynomial:
$$x^2-7x+10$$
the product of zeroes is:
A) $$7$$
B) $$10$$
C) $$-7$$
D) $$-10$$
Answer:
$$10$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The product of zeroes depends only on the constant term and leading coefficient.
Solution:
Given:
$$a=1,\ c=10$$
Using:
$$\frac{c}{a}$$
$$=\frac{10}{1}$$
$$=10$$
Therefore, the correct answer is:
$$10$$
Exam Tip:
For product of zeroes, look directly at the constant term.
————————————————–
Q3. The sum of zeroes of:
$$x^2+5x+6$$
is:
A) $$5$$
B) $$-5$$
C) $$6$$
D) $$-6$$
Answer:
$$-5$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students must correctly identify the sign of the coefficient.
Solution:
Given:
$$a=1,\ b=5$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{5}{1}$$
$$=-5$$
Therefore, the correct answer is:
$$-5$$
Exam Tip:
Be careful with positive and negative signs while applying formulas.
————————————————–
Q4. The product of zeroes of:
$$2x^2+3x-5$$
is:
A) $$-\frac{5}{2}$$
B) $$\frac{5}{2}$$
C) $$-5$$
D) $$5$$
Answer:
$$-\frac{5}{2}$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The leading coefficient affects the product of zeroes.
Solution:
Given:
$$a=2,\ c=-5$$
Using:
$$\frac{c}{a}$$
$$=\frac{-5}{2}$$
$$=-\frac{5}{2}$$
Therefore, the correct answer is:
$$-\frac{5}{2}$$
Exam Tip:
Always write the fraction in simplest form.
————————————————–
Q5. If a quadratic polynomial is:
$$3x^2-12x+4$$
then the sum of zeroes is:
A) $$4$$
B) $$-4$$
C) $$12$$
D) $$-12$$
Answer:
$$4$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students should learn to apply the formula directly from coefficients.
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:
Always identify the values of $$a$$ and $$b$$ before substitution.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
These formulas are valid for quadratic polynomials where:
$$a \ne 0$$
————————————————–
FAQs
Q. Do we always need to find the actual zeroes?
Answer:
No. The sum and product can be found directly using formulas.
Q. Which coefficient is used for the sum of zeroes?
Answer:
The coefficient of $$x$$.
Q. Which coefficient is used for the product of zeroes?
Answer:
The constant term.
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in:
$$-\frac{b}{a}$$
❌ Using $$b$$ instead of $$c$$ for the product formula.
❌ Incorrectly identifying coefficients.
❌ Arithmetic mistakes during simplification.
————————————————–
Quick Revision Notes
✔ For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ The formulas work only for quadratic polynomials.
✔ Always identify $$a$$, $$b$$, and $$c$$ correctly.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students master the relationship between zeroes and coefficients of quadratic polynomials. Understanding these formulas improves speed, accuracy, and performance in board examinations.
Related links
- 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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