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.

Q1(iii):
Find the value of the polynomial $5x – 4x^2 + 3$ at (iii) $x = 2$

Solution :

Given Variables & Initial Setup

We are given a polynomial in a single variable, $x$. Let us define the polynomial as a function $P(x)$:

$P(x) = 5x - 4x^2 + 3$

The objective is to evaluate this polynomial at the specific domain value $x = 2$. [Per the fundamental theorem of polynomial evaluation, finding the value of a polynomial at a given point requires the direct substitution of that point into the variable, followed by simplification according to the standard order of operations (PEMDAS/BODMAS)].

Step 1: Substitution of the Variable

Substitute $x = 2$ into every instance of $x$ within the polynomial $P(x)$:

$P(2) = 5(2) - 4(2)^2 + 3$

Step 2: Resolution of Exponents

According to the order of operations, exponentiation must be resolved before multiplication. We evaluate the quadratic term $(2)^2$:

$2^2 = 2 \times 2 = 4$

Substituting this back into the equation yields:

$P(2) = 5(2) - 4(4) + 3$

Step 3: Execution of Multiplication

Next, perform the scalar multiplications for both the linear and quadratic terms:

  • Linear term: $5 \times 2 = 10$
  • Quadratic term: $4 \times 4 = 16$

Updating the polynomial expression:

$P(2) = 10 - 16 + 3$

Step 4: Sequential Addition and Subtraction

Finally, evaluate the arithmetic expression from left to right:

$P(2) = (10 - 16) + 3$

$P(2) = -6 + 3$

$P(2) = -3$

Graphical Verification

The polynomial $P(x) = -4x^2 + 5x + 3$ represents a downward-opening parabola [since the leading coefficient $a = -4$ is less than zero]. Evaluating the polynomial at $x = 2$ corresponds to finding the $y$-coordinate of the point on this parabola where the $x$-coordinate is $2$. As calculated, this point exists exactly at $(2, -3)$ on the Cartesian plane.

x P(x) 0 1 2 -3 (2, -3) P(x) = -4x² + 5x + 3

Final Solution: The value of the polynomial $5x - 4x^2 + 3$ at $x = 2$ is $-3$.


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

(177)
Top Tutor
locationImg Purasaiwakkam Otteri, Chennai
experience 10 yrs of Exp students 36 students
greenClock 3569 hrs of classes completed
rsIcon 200 per hour
15 Years of Experience in teaching Spoken English & Academic subjects for Class IX-XII
Online Classes Online Classes

I have a total of 10 years of teaching experience. I am Teaching Online for Overseas and Local Students. My Students are from INDIA, UK, USA, INDONESIA & THAILAND. My passion is Teaching. I am Focusing on CBSE, IGCSE, IB, ICSE,&NIOS,.I have conducted National level conference and workshop, Hands-on-training, Seminar, etc Teaching with Human touch produces a great result. My students of class 10th had proven with good results.

Skills: Mathematics , Social Science and more
Also teaches: Class 12 Tuition, Spoken English and more

(1)
Top Tutor
locationImg Mohkam Pur Kala, Dehradun
experience 8 yrs of Exp students 1 student
Tutor
homeTutions Student's Home
regularClasses Tutor's home

5 years experience in teaching in math and science

Skills: English , Mathematics and more
Also teaches: Class I-V Tuition, Class 11 Tuition and more

(26)
Top Tutor
locationImg Serlingampally, Hyderabad
experience 20 yrs of Exp students 13 students
greenClock 623 hrs of classes completed
rsIcon 400 per hour
TEACHING IS MY PASSION-I STILL STRIVE TO BETTER MY TEACHING ABILITIES
Online Classes Online Classes
regularClasses Tutor's home

Teaching is my Passion. I have taught Mathematics, Physics and Chemistry to several students during 20+ years of my teaching. Many of my students who initially were scarred of Mathematics, have developed interest on the subject and opted MPC group in their Intermediate and are now earning Dollars as Software Engineers in USA, CANADA, UK and Australia.

Rajesh

It has been good experience so far. I would request you to resolve last year's question papers chapter wise as on when you progress on chapter. It will help her to keep thorough preparation for term exam as well as board . Also , request you to take exam chapter wise from your end . Is it possible to take 2 hours class together on Saturday instead of taking one hour class on Sunday. Please let us know.

Skills: Mathematics , Physics and more
Also teaches: Class 6 Tuition, Class 7 Tuition and more

(9)
Top Tutor
locationImg Sonari, Jamshedpur
experience 1 yrs of Exp students 4 students
greenClock 657 hrs of classes completed
rsIcon 300 per hour
Online Classes Online Classes
homeTutions Student's Home
regularClasses 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.

Dipali Nagila

Wonderful experience part one month. Look forward to taking more classes with sir. Like the dedicated teaching style.

Skills: Mathematics , Physics and more
Also teaches: Class 9 Tuition, Class 8 Tuition and more

(7)
Top Tutor
locationImg Kharodi West, Mumbai
experience 10 yrs of Exp students 1 student
rsIcon 700 per hour
Commerce graduate with more then 10 years experience
homeTutions Student's Home

An accommodating and versatile individual with the talent to develop inspiring hands-on lessons that will capture a child's imagination and breed success.

Khushi Baxi

She’s the sweetest and the most lovable teacher i have ever met. The subject never felt tough with her.

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