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(iii):
Find the zero of the polynomial in each of the following cases: (iii) $p(x) = 2x + 5$

Solution :

Given Variables & Initial Setup

We are given the linear polynomial:

$p(x) = 2x + 5$

In algebra, the zero of a polynomial is defined as the specific value of the variable (in this case, $x$) that makes the value of the entire polynomial equal to zero. Geometrically, this corresponds to the x-coordinate of the point where the graph of the polynomial intersects the x-axis (the x-intercept).

Step 1: Formulating the Equation

To find the zero of the polynomial, we must equate the polynomial function $p(x)$ to $0$. [Per the Fundamental Theorem of Algebra, a polynomial of degree 1 will have exactly one real zero].

$p(x) = 0$

Substituting the given expression for $p(x)$:

$2x + 5 = 0$

Step 2: Algebraic Isolation of the Variable

We must isolate $x$ using standard algebraic operations.

  • Step 2a: Subtract $5$ from both sides of the equation to isolate the term containing $x$ [By the Subtraction Property of Equality].
    $2x = -5$
  • Step 2b: Divide both sides by $2$ to solve for $x$ [By the Division Property of Equality].
    $x = \frac{-5}{2}$

This fraction can also be expressed as the decimal $-2.5$.

Step 3: Geometric Representation (Visual Proof)

Graphing the linear equation $y = 2x + 5$ provides a visual confirmation of the zero. The line crosses the x-axis exactly at $x = -2.5$.

X Y 0 y = 2x + 5 (0, 5) (-2.5, 0)

Step 4: Verification

To ensure absolute mathematical rigor, we substitute $x = -\frac{5}{2}$ back into the original polynomial to verify that it yields $0$.

$p\left(-\frac{5}{2}\right) = 2\left(-\frac{5}{2}\right) + 5$

$p\left(-\frac{5}{2}\right) = -5 + 5$

$p\left(-\frac{5}{2}\right) = 0$

Since the result is exactly zero, the calculated value is verified as correct.

Final Solution: The zero of the polynomial $p(x) = 2x + 5$ is $x = -\frac{5}{2}$.


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

(9)
Top Tutor
locationImg Bavdhan Vidnyan Nagar, Pune
experience 5 yrs of Exp students 1 student
greenClock 54 hrs of classes completed
rsIcon 250 per hour
You can visit my blog and call me directly at 7709072277
Online Classes Online Classes
regularClasses Tutor's home

I have taught in an institution to state ,ICSE , CBSE kids. Extra-ordinary Results. Ample of Study Material will be provided. We can have a demo class . You would enjoy the interactive and interesting sessions.

Vikram Singh

My experience with Parag sir was great, It is because of him that I got really good grades in my 10th and 12th standard.

Skills: English , Mathematics and more

locationImg Indirapuram Ahinsa Khand 1, Ghaziabad
experience 3 yrs of Exp
Friendly home tutor, who teaches french and and all the other basic subjects at flexible timings!
Online Classes Online Classes
homeTutions Student's Home

I am a professional french tutor with 5 years of experience in teaching languages. I can teach efficiently to all school students as well as adults, for delf-dalf, migration, jobs and other purposes. Over my years teaching, I have been know to be amiable amd flexible according to my students' needs. I always schedule a free demo session for the student to get comfortable with me my teaching techniques and vice versa. The classes I conduct are via offline and online mode both, as preferred.

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

(16)
Top Tutor
locationImg Ashok Nagar D' Souza Layout, Bangalore
experience 7 yrs of Exp students 9 students
greenClock 217 hrs of classes completed
rsIcon 300 per hour
Guiding Minds, Shaping Futures, Inspiring
Online Classes Online Classes

I am an experienced , qualified with experience of 5 years , across different boards including CBSE, ICSE, IGCSE and State Board. Passionate about teaching, over the years I have helped thousands of students .

Skills: Mathematics , Physics and more
Also teaches: Class 12 Tuition, NEET-UG Coaching and more

(40)
Top Tutor
locationImg Godrej Garden City, Ahmedabad
experience 6 yrs of Exp students 20 students
greenClock 1554 hrs of classes completed
rsIcon 500 per hour
B.E. with 6 yrs exp for CBSE/GSEB MATHS-Science
Online Classes Online Classes

I’m a Teacher having 5years experience and offering Home/Online tution of Mathematics & Science for CBSE/ GSEB Students of class 8 to 12. I’m Bachelor of Engineer. My teaching / coaching / mentoring style is such that the students can start and accelerate from whatever their current level. I am sure with my right efforts an average students also will be transformed into best performer.

Rajesh koduru

His classes were very useful as they helped me get good marks in cbse 10th, maths. He is very disciplined and approachable.

Skills: Mathematics , Physics and more
Also teaches: Class 12 Tuition, NEET-UG Coaching and more

(10)
Top Tutor
locationImg Civil Lines, Prayagraj
experience 6 yrs of Exp students 3 students
greenClock 232 hrs of classes completed
rsIcon 300 per hour
#Learn Smoothly & live Happily
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I am a tutor with 6 years experience, academically b.Sc. , b.Ed. , m.A. & ctet qualified. I love to solve problems of students and help them in getting calm and cool. I welcome you with your problems on this account. Wish you a very very nice learning journey.

Afiya Shaikh

I loved animesh sir's teaching sense and am really really blessed to have a tutor like this in my life the most thing about animesh sir I like is that he waits for children he's like type of take your time and he explains again and again he's not at all rude and I guess yess he is gonna be successful in his further life and I wish that may god fulfill his dreams and I request to all the children that you really must take classes from animesh sir if you're very very serious for your studies and what all I appreciate him is very less because he cannot be described in words all of that I want to just say is that I really really like and love animesh sir just because he makes understand and teaches so well, god bless animesh sir with his safe and happy life. Good luck all the best sir for your all examinations and all of the challenges incoming in your life may you be the 1st division in all of them thanks a lot sir for even making children comfortable with you.

Skills: Mathematics , Social Science and more
Also teaches: Class I-V Tuition, Class 6 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 »