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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Solve advanced board exam questions on zeroes of polynomials, missing coefficients, sum and product of zeroes, and polynomial formation with detailed solutions and exam tips.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Advanced Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
This advanced practice set is designed for students who have already learned the basic concepts of polynomials, zeroes, and the relationship between zeroes and coefficients. The questions in this set require deeper conceptual understanding and careful application of formulas. Such questions are commonly seen in board examinations and scholarship tests because they test analytical thinking rather than simple memorization.
What You Will Learn?
✔ Advanced Sum of Zeroes Questions
✔ Advanced Product of Zeroes Questions
✔ Missing Coefficient Problems
✔ Polynomial Formation
✔ Reverse Formula Applications
✔ Board Exam Preparation
Why This Topic Is Important?
Advanced polynomial questions help students develop confidence in handling unfamiliar exam problems and improve mathematical reasoning skills.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. If the sum of zeroes of:
$$3x^2+kx+7$$
is:
$$5$$
then the value of:
$$k$$
is:
A) $$15$$
B) $$-15$$
C) $$5$$
D) $$-5$$
Answer:
$$-15$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The coefficient of $$x$$ can be determined directly from the sum of zeroes.
Solution:
Given:
$$a=3$$
and:
$$-\frac{k}{3}=5$$
Multiplying both sides by:
$$3$$
$$-k=15$$
$$k=-15$$
Therefore, the correct answer is:
$$-15$$
Exam Tip:
In reverse-formula questions, solve carefully for the unknown coefficient.
————————————————–
Q2. If the product of zeroes of:
$$4x^2+9x+k$$
is:
$$3$$
then the value of:
$$k$$
is:
A) $$12$$
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 found directly from the product formula.
Solution:
Given:
$$\frac{k}{4}=3$$
Multiplying both sides by:
$$4$$
$$k=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Remember that the product formula uses only $$a$$ and $$c$$.
————————————————–
Q3. If the zeroes of a quadratic polynomial are:
$$4,\ 7$$
then the polynomial is:
A) $$x^2-11x+28$$
B) $$x^2+11x+28$$
C) $$x^2-28x+11$$
D) $$x^2+28x+11$$
Answer:
$$x^2-11x+28$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Concept Behind This Question:
A polynomial can be formed directly from its zeroes.
Solution:
Given zeroes:
$$4,\ 7$$
Sum:
$$4+7=11$$
Product:
$$4\times7=28$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
$$x^2-11x+28$$
Therefore, the correct answer is:
$$x^2-11x+28$$
Exam Tip:
Calculate the sum and product separately to avoid mistakes.
————————————————–
Q4. If the sum of zeroes is:
$$10$$
and the product of zeroes is:
$$21$$
then the polynomial is:
A) $$x^2-10x+21$$
B) $$x^2+10x+21$$
C) $$x^2-21x+10$$
D) $$x^2+21x+10$$
Answer:
$$x^2-10x+21$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\text{sum})x+(\text{product})$$
Concept Behind This Question:
The standard polynomial form can be created directly from the given conditions.
Solution:
Given:
Sum:
$$10$$
Product:
$$21$$
Using:
$$x^2-(10)x+21$$
$$x^2-10x+21$$
Therefore, the correct answer is:
$$x^2-10x+21$$
Exam Tip:
This is one of the most frequently asked board-level question types.
————————————————–
Q5. For the polynomial:
$$2x^2-9x+k$$
if the product of zeroes is:
$$5$$
then the value of:
$$k$$
is:
A) $$5$$
B) $$10$$
C) $$-10$$
D) $$-5$$
Answer:
$$10$$
Useful Formula for this Question:
Product of zeroes:
$$\frac{c}{a}$$
Concept Behind This Question:
Students should be comfortable using product formulas to find missing constants.
Solution:
Given:
$$a=2$$
and:
$$\frac{k}{2}=5$$
Multiplying both sides by:
$$2$$
$$k=10$$
Therefore, the correct answer is:
$$10$$
Exam Tip:
Always identify the value of $$a$$ before applying the formula.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
For zeroes:
$$\alpha,\ \beta$$
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Reverse Formula:
$$b=-a \times (\text{sum of zeroes})$$
$$c=a \times (\text{product of zeroes})$$
————————————————–
FAQs
Q. Are reverse-formula questions important for board exams?
Answer:
Yes. They are among the most common conceptual questions in Chapter 2.
Q. Can we find unknown coefficients without finding the actual zeroes?
Answer:
Yes. The relationship formulas allow us to do so directly.
Q. Why should students practice advanced questions?
Answer:
Advanced questions improve analytical thinking and exam readiness.
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in the sum formula.
❌ Using the wrong coefficient while applying formulas.
❌ Confusing sum and product formulas.
❌ Making sign errors while forming polynomials.
————————————————–
Quick Revision Notes
✔ Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
✔ Reverse formula:
$$b=-a \times (\text{sum})$$
$$c=a \times (\text{product})$$
✔ Board exams often test reverse applications of formulas.
————————————————–
Conclusion:
These advanced Class 10 Maths Chapter 2 Polynomials MCQs help students strengthen their understanding of polynomial relationships, missing coefficients, and polynomial formation. Consistent practice of such questions builds confidence and improves board exam performance.
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