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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn sum and product of zeroes, missing coefficients, and quadratic polynomial concepts 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 to Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
The relationship between the zeroes and coefficients of a quadratic polynomial is one of the most scoring topics in Class 10 Mathematics. Students should not only know the formulas but also understand how to use them to find missing coefficients and solve reverse-type questions. This practice set focuses on board-level applications of the formulas through carefully designed MCQs and detailed solutions.
What You Will Learn?
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Finding Missing Coefficients
✔ Reverse Formula Applications
✔ Quadratic Polynomial Analysis
✔ Board Exam Preparation
Why This Topic Is Important?
Many board exam questions are based on applying formulas in reverse. Students who master these concepts can solve questions quickly and accurately.
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:
$$4x^2-20x+9$$
is:
A) $$5$$
B) $$-5$$
C) $$9$$
D) $$-9$$
Answer:
$$5$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The sum depends on the coefficients of $$x^2$$ and $$x$$ only.
Solution:
Given:
$$a=4,\ b=-20$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-20}{4}$$
$$=\frac{20}{4}$$
$$=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Ignore the constant term when calculating the sum of zeroes.
Q2. The product of zeroes of:
$$4x^2-20x+9$$
is:
A) $$\frac{9}{4}$$
B) $$-\frac{9}{4}$$
C) $$4$$
D) $$9$$
Answer:
$$\frac{9}{4}$$
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:
$$a=4,\ c=9$$
Using:
$$\frac{c}{a}$$
$$=\frac{9}{4}$$
Therefore, the correct answer is:
$$\frac{9}{4}$$
Exam Tip:
For product questions, the coefficient of $$x$$ is not required.
Q3. If the sum of zeroes of a quadratic polynomial is:
$$6$$
and:
$$a=2$$
then the coefficient of $$x$$ is:
A) $$12$$
B) $$-12$$
C) $$6$$
D) $$-6$$
Answer:
$$-12$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Board exams often ask students to find unknown coefficients using the formula in reverse.
Solution:
Given:
$$-\frac{b}{2}=6$$
Multiplying both sides by:
$$2$$
$$-b=12$$
$$b=-12$$
Therefore, the coefficient of $$x$$ is:
$$-12$$
Hence, the correct answer is:
$$-12$$
Exam Tip:
Reverse-formula questions are common in examinations.
Q4. If the product of zeroes of a quadratic polynomial is:
$$5$$
and:
$$a=3$$
then the constant term is:
A) $$15$$
B) $$-15$$
C) $$5$$
D) $$3$$
Answer:
$$15$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
Students should learn how to find missing coefficients from given information.
Solution:
Given:
$$\frac{c}{3}=5$$
Multiplying both sides by:
$$3$$
$$c=15$$
Therefore, the constant term is:
$$15$$
Hence, the correct answer is:
$$15$$
Exam Tip:
Cross-multiplication is often the quickest method in such questions.
Q5. For the polynomial:
$$5x^2+bx+20$$
if the sum of zeroes is:
$$-3$$
then the value of:
$$b$$
is:
A) $$15$$
B) $$-15$$
C) $$3$$
D) $$-3$$
Answer:
$$15$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students must be comfortable finding unknown coefficients using algebraic manipulation.
Solution:
Given:
$$a=5$$
and:
$$-\frac{b}{5}=-3$$
Multiplying both sides by:
$$5$$
$$-b=-15$$
$$b=15$$
Therefore, the correct answer is:
$$15$$
Exam Tip:
Always keep track of negative signs while solving reverse-formula questions.
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
Reverse Formula:
If sum of zeroes is known:
$$b=-a \times (\text{sum of zeroes})$$
If product of zeroes is known:
$$c=a \times (\text{product of zeroes})$$
FAQs
Q. Can board exams ask missing coefficient questions?
Answer:
Yes. Such questions are frequently asked because they test conceptual understanding.
Q. Is it necessary to find actual zeroes?
Answer:
No. The formulas provide the required information directly.
Q. Which formula is used to find the coefficient of $$x$$?
Answer:
The sum of zeroes formula:
$$-\frac{b}{a}$$
Common Mistakes Students Make
❌ Forgetting negative signs.
❌ Confusing sum and product formulas.
❌ Incorrect cross-multiplication.
❌ Not simplifying answers completely.
Quick Revision Notes
✔ Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ Reverse formula for coefficient:
$$b=-a \times (\text{sum})$$
✔ Reverse formula for constant term:
$$c=a \times (\text{product})$$
✔ Board exams often include reverse-formula questions.
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students master both direct and reverse applications of the relationship between zeroes and coefficients. Regular practice of such questions improves conceptual understanding and board exam performance.
Related links
- 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
- 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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