default_background
✕

Find the best tutors and institutes for Class 10 Tuition

Find Best Class 10 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Q4(ii):
Find the zero of the polynomial in each of the following cases: (ii) $p(x) = x – 5$

Solution :

Given Polynomial & Theoretical Foundation

We are tasked with finding the zero of the following linear polynomial:

$p(x) = x - 5$

Step 1: Applying the Definition of a Zero

The zero (or root) of a polynomial $p(x)$ is defined as the specific real value of the variable $x$ for which the polynomial evaluates to zero. [Per the fundamental definition of polynomial roots]. Therefore, to find the zero, we must set the polynomial equal to zero:

$p(x) = 0$

Step 2: Algebraic Substitution and Manipulation

Substituting the given algebraic expression for $p(x)$ into our equation, we obtain:

$x - 5 = 0$

To isolate the variable $x$ and solve the linear equation, we add $5$ to both sides of the equation [Per the Addition Property of Equality, which states that adding the same number to both sides of an equation maintains its balance]:

$x - 5 + 5 = 0 + 5$

$x = 5$

Step 3: Rigorous Verification

To ensure absolute mathematical accuracy, we verify the solution by substituting $x = 5$ back into the original polynomial to check if it yields zero:

$p(5) = (5) - 5$

$p(5) = 0$

Since the evaluation results in exactly zero, $x = 5$ is confirmed as the correct zero of the polynomial.

Step 4: Graphical Interpretation

Geometrically, the zero of a polynomial with real coefficients corresponds to the $x$-coordinate of the point where the graph of the function $y = p(x)$ intersects the $x$-axis (where $y = 0$). For the linear function $y = x - 5$, the $x$-intercept occurs exactly at the Cartesian coordinate $(5, 0)$.

x y 0 y = x - 5 (0, -5) Zero: (5, 0)

Final Solution: The zero of the polynomial $p(x) = x - 5$ is $x = 5$.


More Questions from Class 9 Mathematics Polynomials EXERCISE 2.2


CBSE Solutions for Class 9 Mathematics Polynomials


Chapters in CBSE - Class 9 Mathematics


Top Tutors who teach Polynomials

(11)
Top Tutor
locationImg Melakalkandarkottai, Tiruchirappalli
experience 10 yrs of Exp students 1 student
greenClock 17 hrs of classes completed
rsIcon 300 per hour
M.Sc.,B.Ed. with 13 years of teaching experience
Online Classes Online Classes
homeTutions Student's Home

I specialize in Class 10 Mathematics tuition with an exam-oriented and concept-based teaching approach. I simplify complex mathematical concepts using step-by-step explanations, making them easy for students to understand and apply confidently. I assess each student's learning level, identify weak areas, and provide personalized guidance to improve both accuracy and speed. My classes include regular practice, chapter-wise tests, previous years' board exam questions, doubt-clearing sessions, and effective exam strategies. I maintain a friendly and motivating learning environment where students feel comfortable asking questions. My objective is to help every student strengthen their mathematical foundation, gain confidence, and achieve excellent results in the Class 10 board examinations.

Skills: Mathematics

(8)
Top Tutor
locationImg Anna Nagar Western Extn, Chennai
experience 7 yrs of Exp students 3 students
greenClock 48 hrs of classes completed
rsIcon 500 per hour
Mathematics class for school students 6 year experience m.sc,b ed
homeTutions Student's Home
regularClasses Tutor's home

I am an experienced, qualified teacher and tutor with over 6 years of experience in teaching Maths across different boards including CBSE, ICSE, IGCSE and State Board. Passionate about solving mathematical problems. over the years I have helped hundred of students overcome their fear of Maths. I am a post graduates in mathematics and under graduates in education. We are available on both home tuition and online We have lot of success stories.

Skills: Mathematics
Also teaches: ICWA(CMA) Coaching, Class 8 Tuition and more

(27)
Top Tutor
locationImg Gaur City 2, Noida
experience 8 yrs of Exp students 1 student
greenClock 388 hrs of classes completed
rsIcon 100 per hour
"Experienced & certified Maths tutor with 8 years of experience in teaching mathematics"
Online Classes Online Classes

Maths tutor with 8 years of experience in teaching maths at SGB Coaching Institute Mau Uttar Pradesh.

Skills: Mathematics
Also teaches: Class 12 Tuition, Class 11 Tuition and more

Dr apoorva S. Class 10 Tuition trainer in Roorkee
(17)
Top Tutor
locationImg Roorkee, Roorkee
experience 5 yrs of Exp students 6 students
greenClock 111 hrs of classes completed
rsIcon 350 per hour
Experienced educator with 5+ years of teaching experience
Online Classes Online Classes

An experienced educator with over 5 years of teaching experience, I have had the privilege of mentoring more than 100 students. My expertise spans foundational high school courses (9th–10th Science, 11th–12th Biology) as well as advanced engineering disciplines (B.Tech & M.Tech). I hold a B.Tech, M.Tech, and Ph.D. in Biotechnology, alongside a competitive GATE qualification. My approach focuses on building deep conceptual clarity and critical thinking, followed by structured problem-solving, regular assessments, and rigorous PYQ practice. This exam-focused strategy ensures students achieve outstanding performance in both board exams and competitive tests.

Alokik Saini

Honestly, my experience at TTN Classes – Vigyan Classes has been really good 😊. Dr. Apoorva Singh Ma’am teaches very well πŸ“š and explains every concept in a simple and easy-to-understand way. Her classes are informative, interactive, and enjoyable πŸ˜„. She is very friendly and supportive with students 🀝, clears doubts patiently, and always motivates us to do better πŸ’―. She also gives career counselling and guidance🎯, which really helps students understand their options and make better decisions about their future. I also really enjoy the celebrations πŸŽ‰ we have on different occasions like birthdays πŸŽ‚, results πŸ†, and other events.These moments make the classes more memorable and create a great bond between students and teachers ❀️. Overall, I genuinely enjoy studying at Vigyan Classes. Great teaching πŸ‘©β€πŸ«, career guidance 🎯, a friendly environment 😊, and lots of memorable moments πŸŽ‰. Definitely a great experience!

Skills: Physics , Chemistry and more
Also teaches: Class 9 Tuition, Class 12 Tuition and more

(9)
Top Tutor
locationImg BRS Nagar, Ludhiana
greenClock 27 hrs of classes completed
English teacher with spoken and communication skills
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I was a student in one of the top colleges of Ludhiana. I have proficiency in English . I can teach all subjects to primary wing .

Skills: English , Mathematics and more
Also teaches: Class 8 Tuition, Class 11 Tuition and more

Find more Tutor for Polynomials in your City


Other Subjects in CBSE - Class 9

Worksheet Icon

Download free CBSE - Class 9 Mathematics Polynomials EXERCISE 2.2 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »