Welcome To My School Study
Practice Class 10 Maths Chapter 2 Polynomials, forming quadratic polynomials MCQ Questions with Answers based on NCERT syllabus. Solve mixed board exam questions on zeroes of polynomials, relationship between zeroes and coefficients with detailed solutions and exam tips.
Do You Know
Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Board Exam Level
Based On: NCERT Latest Syllabus
Introduction:
By this stage, students have learned the basics of polynomials, zeroes of polynomials, the relationship between zeroes and coefficients, and the formation of quadratic polynomials from given zeroes. This practice set combines all these concepts into one mixed revision exercise. Such mixed questions are very common in school tests and board examinations because they test conceptual understanding rather than memorization.
What You Will Learn?
✔ Finding Zeroes
✔ Sum and Product of Zeroes
✔ Forming Quadratic Polynomials
✔ Relationship Between Zeroes and Coefficients
✔ Board Exam Problem Solving
✔ Mixed Concept Revision
Why This Topic Is Important?
Mixed-concept questions improve problem-solving skills and help students apply formulas correctly in different situations.
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:
$$x^2-11x+24$$
is:
A) $$11$$
B) $$24$$
C) $$-11$$
D) $$-24$$
Answer:
$$11$$
Useful Formula for this Question:
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Concept Behind This Question:
The sum of zeroes depends only on the coefficients of $$x^2$$ and $$x$$.
Solution:
Given:
$$a=1,\ b=-11$$
Using:
$$-\frac{b}{a}$$
$$=-\frac{-11}{1}$$
$$=11$$
Therefore, the correct answer is:
$$11$$
Exam Tip:
Ignore the constant term while finding the sum of zeroes.
————————————————–
Q2. The product of zeroes of:
$$x^2-11x+24$$
is:
A) $$11$$
B) $$24$$
C) $$-11$$
D) $$-24$$
Answer:
$$24$$
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:
$$a=1,\ c=24$$
Using:
$$\frac{c}{a}$$
$$=\frac{24}{1}$$
$$=24$$
Therefore, the correct answer is:
$$24$$
Exam Tip:
For monic polynomials, the product equals the constant term.
————————————————–
Q3. If the zeroes of a quadratic polynomial are:
$$1,\ 6$$
then the polynomial is:
A) $$x^2-7x+6$$
B) $$x^2+7x+6$$
C) $$x^2-6x+7$$
D) $$x^2+6x+7$$
Answer:
$$x^2-7x+6$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Concept Behind This Question:
The sum and product of zeroes help form the polynomial directly.
Solution:
Given zeroes:
$$1,\ 6$$
Sum:
$$1+6=7$$
Product:
$$1\times6=6$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
$$x^2-7x+6$$
Therefore, the correct answer is:
$$x^2-7x+6$$
Exam Tip:
Always calculate the sum and product separately before forming the polynomial.
————————————————–
Q4. Which of the following is a zero of:
$$p(x)=x^2-16$$
A) $$2$$
B) $$3$$
C) $$4$$
D) $$5$$
Answer:
$$4$$
Useful Formula for this Question:
A zero satisfies:
$$p(x)=0$$
Concept Behind This Question:
Substitution helps verify whether a number is a zero.
Solution:
Substitute:
$$x=4$$
$$p(4)=4^2-16$$
$$=16-16$$
$$=0$$
Therefore:
$$4$$
is a zero of the polynomial.
Hence, the correct answer is:
$$4$$
Exam Tip:
Whenever substitution gives zero, the value is a zero.
————————————————–
Q5. If the sum of zeroes is:
$$9$$
and the product of zeroes is:
$$20$$
then the quadratic polynomial is:
A) $$x^2-9x+20$$
B) $$x^2+9x+20$$
C) $$x^2-20x+9$$
D) $$x^2+20x+9$$
Answer:
$$x^2-9x+20$$
Useful Formula for this Question:
Polynomial:
$$x^2-(\text{sum})x+(\text{product})$$
Concept Behind This Question:
A polynomial can be formed directly from the sum and product of its zeroes.
Solution:
Given:
Sum:
$$9$$
Product:
$$20$$
Using:
$$x^2-(\text{sum})x+(\text{product})$$
$$x^2-9x+20$$
Therefore, the correct answer is:
$$x^2-9x+20$$
Exam Tip:
This is one of the most common board examination question patterns.
————————————————–
Important Formulas and Concepts
For:
$$ax^2+bx+c$$
Sum of zeroes:
$$-\frac{b}{a}$$
Product of zeroes:
$$\frac{c}{a}$$
For zeroes:
$$\alpha,\ \beta$$
Quadratic Polynomial:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
Alternative Form:
$$x^2-(\text{sum})x+(\text{product})$$
————————————————–
FAQs
Q. Can a board exam contain mixed-concept questions?
Answer:
Yes. Most board papers contain questions that combine multiple concepts.
Q. What is the fastest way to form a polynomial?
Answer:
Use the sum and product of zeroes directly in the standard formula.
Q. How can a zero be verified?
Answer:
Substitute the value into the polynomial and check whether the result becomes:
$$0$$
————————————————–
Common Mistakes Students Make
❌ Forgetting the negative sign in the sum formula.
❌ Confusing sum and product.
❌ Sign errors while forming polynomials.
❌ Not verifying zeroes through substitution.
————————————————–
Quick Revision Notes
✔ Sum of zeroes:
$$-\frac{b}{a}$$
✔ Product of zeroes:
$$\frac{c}{a}$$
✔ Polynomial from zeroes:
$$x^2-(\alpha+\beta)x+\alpha\beta$$
✔ Verify a zero by substitution.
✔ Practice mixed-concept questions regularly.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs provide mixed-concept practice covering all major topics of the chapter. Regular revision of such questions helps students improve speed, accuracy, and confidence for board examinations.
Related links
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- 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 Social Science : Consumer Rights, RTI & Water Resources
- Class 10 Social Science: Project Tiger, Green Revolution
Latest Posts
- Who was Isaac Newton? – Life, Discoveries, Laws of Motion & Gravity
- Class 9 Maths Chapter 3 Coordinate Geometry
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
- Class 7 Maths Chapter 2 Fractions and Decimals
- Class 8 Maths Chapter 3 Understanding Quadrilaterals
Join Our Other Communities
Instagram , Youtube , Facebook
