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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, reverse formula applications, and missing coefficient problems 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 allows students to solve many questions quickly without finding the actual zeroes. In board examinations, questions are often asked where students must determine unknown coefficients using the sum or product of zeroes. This practice set focuses on these important applications and helps strengthen algebraic reasoning skills.
What You Will Learn?
✔ Sum of Zeroes
✔ Product of Zeroes
✔ Finding Missing Coefficients
✔ Reverse Formula Applications
✔ Quadratic Polynomial Concepts
✔ Board Exam Preparation
Why This Topic Is Important?
These concepts are frequently tested in board exams and form the foundation for advanced algebraic problem-solving.
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:
$$6x^2-18x+7$$
is:
A) $$3$$
B) $$-3$$
C) $$7$$
D) $$-7$$
Answer:
$$3$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The coefficient of $$x$$ determines the sum of zeroes.
Solution:
Given:
$$a=6,\ b=-18$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-18}{6}$$
$$=\frac{18}{6}$$
$$=3$$
Therefore, the correct answer is:
$$3$$
Exam Tip:
Always simplify the fraction completely.
————————————————–
Q2. The product of zeroes of:
$$6x^2-18x+7$$
is:
A) $$\frac{7}{6}$$
B) $$-\frac{7}{6}$$
C) $$7$$
D) $$6$$
Answer:
$$\frac{7}{6}$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The product depends on the constant term and leading coefficient.
Solution:
Given:
$$a=6,\ c=7$$
Using:
$$\frac{c}{a}$$
$$=\frac{7}{6}$$
Therefore, the correct answer is:
$$\frac{7}{6}$$
Exam Tip:
The coefficient of $$x$$ is not needed for the product formula.
————————————————–
Q3. For the polynomial:
$$2x^2+bx+9$$
if the sum of zeroes is:
$$4$$
then the value of:
$$b$$
is:
A) $$-8$$
B) $$8$$
C) $$4$$
D) $$-4$$
Answer:
$$-8$$
Useful Formula for this Question:
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
Students should be able to find unknown coefficients from the given sum.
Solution:
Given:
$$a=2$$
and:
$$-\frac{b}{2}=4$$
Multiplying both sides by:
$$2$$
$$-b=8$$
$$b=-8$$
Therefore, the correct answer is:
$$-8$$
Exam Tip:
Keep track of negative signs while solving reverse-formula questions.
————————————————–
Q4. For the polynomial:
$$4x^2+7x+c$$
if the product of zeroes is:
$$3$$
then the value of:
$$c$$
is:
A) $$7$$
B) $$12$$
C) $$3$$
D) $$4$$
Answer:
$$12$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
The constant term can be determined directly from the product formula.
Solution:
Given:
$$a=4$$
and:
$$\frac{c}{4}=3$$
Multiplying both sides by:
$$4$$
$$c=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Use cross-multiplication to save time.
————————————————–
Q5. If the sum of zeroes is:
$$-5$$
and the product of zeroes is:
$$6$$
then the quadratic polynomial is:
A) $$x^2+5x+6$$
B) $$x^2-5x+6$$
C) $$x^2+5x-6$$
D) $$x^2-5x-6$$
Answer:
$$x^2+5x+6$$
Useful Formula for this Question:
For a monic quadratic polynomial:
$$x^2-(\text{sum})x+(\text{product})$$
Concept Behind This Question:
The sum and product of zeroes can be used to form a quadratic polynomial directly.
Solution:
Given:
Sum of zeroes:
$$-5$$
Product of zeroes:
$$6$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
Substituting:
$$x^2-(-5)x+6$$
$$=x^2+5x+6$$
Therefore, the correct answer is:
$$x^2+5x+6$$
Exam Tip:
When the sum is negative, the sign changes after substitution.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
For a monic quadratic polynomial:
$$x^2-(\text{sum of zeroes})x+(\text{product of zeroes})$$
Reverse Formula:
$$b=-a \times (\text{sum of zeroes})$$
$$c=a \times (\text{product of zeroes})$$
————————————————–
FAQs
Q. Can a quadratic polynomial be formed from the sum and product of zeroes?
Answer:
Yes. For a monic polynomial, use:
$$x^2-(\text{sum})x+(\text{product})$$
Q. Are reverse-formula questions important for board exams?
Answer:
Yes. They are commonly asked because they test conceptual understanding.
Q. Which formula is used to find the constant term?
Answer:
$$\frac{c}{a}=\text{product of zeroes}$$
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in the sum formula.
❌ Using the wrong coefficient in calculations.
❌ Making sign errors while forming a polynomial.
❌ Confusing sum and product formulas.
————————————————–
Quick Revision Notes
✔ Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ Form quadratic polynomial:
$$x^2-(\text{sum})x+(\text{product})$$
✔ Reverse formula:
$$b=-a \times (\text{sum})$$
$$c=a \times (\text{product})$$
✔ Check signs carefully.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs strengthen students’ understanding of the relationship between zeroes and coefficients. Regular practice of such questions improves algebraic thinking, speed, and accuracy for board examinations.
Related links
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