Find the best tutors and institutes for Class 10 Tuition
Q2(iv):
Write the coefficients of $x^2$ in each of the following:
(iv) $\sqrt{2}x - 1$
Solution :
Initial Setup & Theoretical Foundation
We are given the algebraic expression:
$P(x) = \sqrt{2}x - 1$
Our objective is to determine the coefficient of the $x^2$ term within this polynomial. [By definition, a coefficient is the numerical multiplier of a variable in a specific term of an algebraic expression].
Step 1: Analyzing the Degree and Terms of the Polynomial
The given polynomial, $P(x) = \sqrt{2}x - 1$, consists of two explicitly written terms:
- The linear term: $\sqrt{2}x$, where the variable $x$ is raised to the power of $1$. The coefficient here is $\sqrt{2}$.
- The constant term: $-1$, which can be mathematically expressed as $-1x^0$.
Because the highest power of the variable $x$ present in the expression is $1$, this is classified as a linear polynomial (degree $1$).
Step 2: Expressing the Polynomial in Standard Form
To rigorously identify the coefficient of a term that does not explicitly appear in the expression (in this case, the $x^2$ term), we must rewrite the polynomial in its complete standard descending form. [Per the axioms of polynomial representation, any missing term of degree $k$ can be introduced into the expression by multiplying it by zero ($0 \cdot x^k$), because adding the additive identity ($0$) does not alter the intrinsic value of the polynomial].
We expand $P(x)$ to explicitly include the quadratic ($x^2$) term:
$P(x) = 0 \cdot x^2 + \sqrt{2}x - 1$
Step 3: Visualizing the Polynomial Structure
The diagram below illustrates the structural breakdown of the polynomial when expanded to include the quadratic term, isolating the coefficient for each degree of $x$.
Step 4: Extracting the Target Coefficient
By comparing our expanded polynomial $P(x) = 0x^2 + \sqrt{2}x - 1$ with the general quadratic form $ax^2 + bx + c$, we can map the coefficients directly:
- $a$ (coefficient of $x^2$) = $0$
- $b$ (coefficient of $x$) = $\sqrt{2}$
- $c$ (constant term) = $-1$
Since the $x^2$ term is entirely absent from the original expression, its numerical multiplier must be zero.
Final Solution: The coefficient of $x^2$ in the polynomial $\sqrt{2}x - 1$ is $0$.
More Questions from Class 9 Mathematics Polynomials EXERCISE 2.1
- Q1(i): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) $4x^2 – 3x + 7$
- Q1(ii): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (ii) $y^2 + \sqrt{2}$
- Q1(iii): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (iii) $3\sqrt{t} + t\sqrt{2}$
- Q1(iv): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (iv) $y + \frac{2}{y}$
- Q1(v): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (v) $x^{10} + y^3 + t^{50}$
- Q2(i): Write the coefficients of $x^2$ in each of the following: (i) $2 + x^2 + x$
- Q2(ii): Write the coefficients of $x^2$ in each of the following: (ii) $2 – x^2 + x^3$
- Q2(iii): Write the coefficients of $x^2$ in each of the following: (iii) $\frac{\pi}{2}x^2 + x$
- Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.
- Q4(i): Write the degree of each of the following polynomials: (i) $5x^3 + 4x^2 + 7x$
- Q4(ii): Write the degree of each of the following polynomials: (ii) $4 – y^2$
- Q4(iii): Write the degree of each of the following polynomials: (iii) $5t – \sqrt{7}$
- Q4(iv): Write the degree of each of the following polynomials: (iv) $3$
- Q5(i): Classify the following as linear, quadratic and cubic polynomials: (i) $x^2 + x$
- Q5(ii): Classify the following as linear, quadratic and cubic polynomials: (ii) $x – x^3$
- Q5(iii): Classify the following as linear, quadratic and cubic polynomials: (iii) $y + y^2 + 4$
- Q5(iv): Classify the following as linear, quadratic and cubic polynomials: (iv) $1 + x$
- Q5(v): Classify the following as linear, quadratic and cubic polynomials: (v) $3t$
- Q5(vi): Classify the following as linear, quadratic and cubic polynomials: (vi) $r^2$
- Q5(vii): Classify the following as linear, quadratic and cubic polynomials: (vii) $7x^3$
CBSE Solutions for Class 9 Mathematics Polynomials
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Polynomials
Top Tutor
Mira Road, Mira-Bhayandar
10 yrs of
Exp
7 students
84 hrs of classes completed
600
per hour
Student's Home
Tutor's home
Math and physics teacher. Expert in cbse education and assessment patten. Been an cbse examiner for 5 continuous years. Aware of the curriculum of ssc, icse and cbse grade 7-10 math and physics. Tutoring since 2006 and been quite successful in giving results.
I would like to say the class was really helpful. I was able to catch a hold on various topics taught in class. Sir also has a very kind nature and he helped us in various way. Overall I loved the class.
Top Tutor
Nerul, Mumbai
10 yrs of
Exp
5 students
640 hrs of classes completed
450
per hour
Online Classes
Student's Home
Tutor's home
I have specifically guided Class 10 students for board exams, with a strong focus on NCERT syllabus, and topics like Real Numbers, Polynomials, Quadratic Equations, and Statistics. I provide regular tests, personalized feedback, and exam-oriented strategies to improve accuracy and speed. Many of my students have shown remarkable improvement and scored above 90% in their board exams.
It was an amazing experience learning and understanding maths with Saurav sir. He really helped me overcome my fear of maths and helped me score good marks in a subject that previously scared me. It really shows how dedicated he is as a teacher. Really good experience!
Top Tutor
Sonari, Jamshedpur
1 yrs of
Exp
4 students
657 hrs of classes completed
300
per hour
Online Classes
Student's Home
Tutor's home
I have a Science background completed my electrical engineering.... I am giving home tuition for 2 years.... I am also preparing for UPSC civil service exam.
Wonderful experience part one month. Look forward to taking more classes with sir. Like the dedicated teaching style.
Top Tutor
Sector-16, Faridabad
1 yrs of
Exp
4 students
532 hrs of classes completed
400
per hour
Online Classes
Student's Home
Tutor's home
I have taught my two sons when they were in class 10. They manged to clear the IIT JEE exam in 1st attempt. I teach by example, which helps the students to visualize the concepts and ideas. I believe in participative learning where the student also gives their viewpoints. This is how they start enjoying the subject and their performance level increases automatically.
My experience so far is great with Sir. He teaches topics very well. He also focuses on the practical applications of the topics.
Carterpuri, Palam Vihar, Gurgaon
20 yrs of
Exp
500
per hour
Student's Home
I am a professional teacher with more than 25 years of teaching experience in prestigious schools of India.My teaching assures value for money and produce best results.I emphasize on concepts clarity and create natural interest in the subject.
Find more Tutor for Polynomials in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
