NCERT Solutions Class 9 Maths Chapter 2 Introduction to Linear Polynomials on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.1#

The degree of a polynomial in one variable is the highest power of that variable that appears with a non-zero coefficient. A non-zero constant has degree $0$, and the polynomials of degree $1, 2, 3$ are called linear, quadratic, cubic, respectively.

1. Find the degrees of the following polynomials: #

(i) 2x² − 5x + 3

Highest power of $x$ is $2$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.2#

Evaluating a polynomial means substituting a specific value for the variable and simplifying. Word problems in this exercise translate everyday statements into a linear equation of the form $ax + b = c$, which is then solved for the unknown.

1. Find the value of the linear polynomial 5x − 3 if: #

Let $p(x) = 5x - 3$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.3#

A quantity that changes by the same fixed amount each step can be written as a linear expression $a n + b$, where $b$ is the starting value and $a$ is the constant change per step (positive for growth, negative for decay).

1. A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month. #

Solution

She starts with ₹500 and adds ₹150 every month, so at the end of the $n^{\text{th}}$ month she has:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.4

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.4#

A relation $y = a t + b$ is called linear because $y$ changes by a constant amount $a$ for each unit change in $t$. If $a > 0$ we call it linear growth; if $a < 0$ we call it linear decay.

1. Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month. #

The plant starts at 1.75 feet and grows 0.5 feet each month, so after $t$ months its height in feet is:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.5

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.5#

To find the constants $a$ and $b$ in $y = a x + b$ from two known points $(x_1, y_1)$ and $(x_2, y_2)$, subtract the two equations to eliminate $b$: $a = \dfrac{y_2 - y_1}{x_2 - x_1}$, then substitute back to get $b$.

1. A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹400. When she accessed 14 modules, her bill was ₹500. If the monthly bill y depends on the number of modules accessed, x, according to the relation y = ax + b, find the values of a and b. #

Solution

When she accessed 10 modules, her bill was ₹400, so:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials Exercise Set 2.6

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.6#

Every equation of the form $y = a x + b$ has a straight-line graph. The number $a$ is the slope (steepness and direction of the line) and $b$ is the y-intercept (the point where the line crosses the y-axis).

1. Draw the graphs of the following sets of lines. In each case, reflect on the role of ‘a’ and ‘b’. #

(i) y = 4x, y = 2x, y = x

Pick a few $x$-values and find $y$:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 2 — End-of-Chapter Exercises#

These problems combine everything from the chapter: writing polynomials of a chosen degree, evaluating polynomials, translating word problems into linear equations, and graphing $y = a x + b$. Key formula used often: for a line through two points $(x_1, y_1)$ and $(x_2, y_2)$, slope $a = \dfrac{y_2 - y_1}{x_2 - x_1}$.

1. Write a polynomial of degree 3 in the variable x, in which the coefficient of the x² term is −7. #

Solution (answers vary)

Any polynomial whose highest power of $x$ is 3 and whose $x^2$ term is $-7x^2$ works. For example: