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.

Q3(ii):
Verify whether the following are zeroes of the polynomial, indicated against them. (ii) $p(x) = 5x – \pi, x = \frac{4}{5}$

Solution :

Given Variables & Initial Setup

We are given the following linear polynomial in one variable:

$p(x) = 5x - \pi$

We are tasked with verifying whether the following specific value of $x$ is a zero (root) of the polynomial:

$x = \frac{4}{5}$

Step 1: Theoretical Foundation

By the fundamental definition of the Zero of a Polynomial [Factor Theorem corollary], a real number $a$ is considered a zero of a polynomial $p(x)$ if and only if evaluating the polynomial at $x = a$ yields exactly zero. Mathematically, this is expressed as:

$p(a) = 0$

Therefore, to verify if $x = \frac{4}{5}$ is a zero, we must substitute $x = \frac{4}{5}$ into $p(x)$ and determine if the resulting value is equal to $0$.

Step 2: Substitution and Algebraic Evaluation

Substitute $x = \frac{4}{5}$ into the polynomial $p(x)$:

$p\left(\frac{4}{5}\right) = 5\left(\frac{4}{5}\right) - \pi$

Perform the multiplication. The factor of $5$ in the numerator and the denominator cancel each other out:

$p\left(\frac{4}{5}\right) = 4 - \pi$

Step 3: Analytical Verification

We must now evaluate the expression $4 - \pi$.

  • The number $4$ is a rational integer.
  • The number $\pi$ is an irrational mathematical constant representing the ratio of a circle's circumference to its diameter, where $\pi \approx 3.14159...$

Because $\pi$ is strictly less than $4$ (and is irrational), the difference $4 - \pi$ evaluates to a non-zero irrational number:

$4 - \pi \approx 4 - 3.14159 = 0.85841 \neq 0$

Evaluated Point ($x$) Polynomial Expression $p(x)$ Resulting Value Is $p(x) = 0$?
$x = \frac{\pi}{5}$ (Actual Zero) $5\left(\frac{\pi}{5}\right) - \pi$ $0$ Yes
$x = \frac{4}{5}$ (Tested Point) $5\left(\frac{4}{5}\right) - \pi$ $4 - \pi \approx 0.858$ No

Step 4: Graphical Representation (Visual Verification)

Graphically, the zeroes of a polynomial $p(x)$ correspond to the $x$-intercepts of the graph $y = p(x)$. The graph below plots the linear function $y = 5x - \pi$. The true zero is located at $x = \frac{\pi}{5} \approx 0.628$, while our tested point $x = \frac{4}{5} = 0.8$ clearly yields a positive $y$-value, proving it does not intersect the $x$-axis at this coordinate.

x y 0 1.0 y = 5x - π Zero: x = π/5 p(4/5) = 4 - π ≠ 0 x = 4/5

Final Solution: Since $p\left(\frac{4}{5}\right) = 4 - \pi \neq 0$, the value $x = \frac{4}{5}$ is NOT a zero of the polynomial $p(x) = 5x - \pi$.


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

Ramakrishna Koutha Class 10 Tuition trainer in Mount Olive
(17)
Top Tutor
locationImg Flanders, Mount Olive
experience 5 yrs of Exp students 2 students
greenClock 22 hrs of classes completed
rsIcon 100 per hour
Experience Software engineer and volunteer teacher in math , science and computer science.
Online Classes Online Classes

I have volunteer teacher for evidyaloka ..I thought higg school students math and science

Skills: Mathematics , Physics and more

Shweta Chaddha Class 10 Tuition trainer in Bangalore
(52)
Top Tutor
locationImg Electronic City Phase I, Bangalore
experience 20 yrs of Exp students 15 students
greenClock 627 hrs of classes completed
rsIcon 300 per hour
I have been teaching school past20 years and i know the right path to guide students
Online Classes Online Classes

I have 20yrs experience for 9to 12th class.

Ishita

She teaches very well. I understand the concept very fast. She teaches smoothly always ask for any doubt. Very polite and calm in nature.

Skills: Mathematics , Science
Also teaches: Class 9 Tuition, Class 6 Tuition and more

(10)
Top Tutor
locationImg Padmanabhanagar, Bangalore
experience 3 yrs of Exp
rsIcon 450 per hour
Spoken English, BTech Tuition, C Language, C++ Language, CAD etc., with 4 years of experience
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I am an experienced tutor with 4 years of experience in this field. I completed my BE in the year 2014. I have tutored students for Spoken English, BTech Tuition, C Language, C++ Language, CAD, CE and COMEDK Coaching. I can conduct classes at Student's Home, My place and Online via a different medium to students from International, CBSE, State, ICSE/ISC Board. I follow different techniques while teaching so, that my students are engaged positively. To make learning fun and easier, I use creative and innovative ideas.

Skills: English , Mathematics and more
Also teaches: CET Coaching, BTech Tuition and more

(12)
Top Tutor
locationImg Nanded, Pune
experience 12 yrs of Exp students 1 student
rsIcon 1000 per hour
I am here for Passion.Best Online Tutor for ICSE, CBSE,IGCSE,IBDP,SAT. Quality Education with Fun
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

Dedicated and passionate educator with over 10 years of experience teaching Mathematics and Science to students of Classes 8th to 12th across multiple boards — CBSE, ICSE, IGCSE, IB MYP, and IBDP. Founder of Ishaan Tuitions, Pune, specializing in personalized one-to-one coaching and small group sessions designed to strengthen conceptual understanding and academic performance. Expertise also includes preparing students for competitive examinations such as SAT and IIT-JEE Mains, with a strong record of improving analytical thinking and problem-solving abilities.

Skills: Mathematics , Physics and more
Also teaches: Class 8 Tuition, SAT Coaching and more

Deepak Joshi Class 10 Tuition trainer in Bangalore
(48)
Top Tutor
locationImg Ashok Nagar D' Souza Layout, Bangalore
experience 10 yrs of Exp students 25 students
greenClock 772 hrs of classes completed
rsIcon 600 per hour
Ph.D. Candidate | M.Sc. (Mathematics) | Former Faculty at BYJU'S (7 Years) & DPS Gurgaon (3 Years)
Online Classes Online Classes

10+ years of experience teaching Mathematics for Grades 10 to 12th • Consistent record of 100% academic results • Very friendly and supportive learning environment • Encourages students to ask questions freely and confidently • Strong focus on conceptual clarity and problem-solving skills • Helps students build confidence and excel in Mathematics • Fee Structure for One-to-One Classes: ₹700 per hour • Group Classes: ₹4,000 per month.

Pratima Dixit

Sir clears all my doubts he makes difficult concepts easy to understand he takes Previous year questions which makes it easier to prepare

Skills: Mathematics
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 »