Polynomials (Exercise 2.1)

Polynomials


Chapter 2


Exercise 2.1


EX 2.1 QUESTION 1.


Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x2–3x+7

(ii) y2+√2

(iii) 3√t+t√2

(iv) y+2/y

(v) x10+y3+t50

Solution:

(i) 4x2–3x+7

The given equation has x is the only variable. So, the polynomial in one variable.

(ii) y2+√2

The given equation has y is the only variable. So, the polynomial in one variable.

(iii) 3√t+t√2

= 3 √t1/2 + √2.t

It is in one variable but not polynomial because it contains (t1/2) which is not a whole number.

(iv) y+2/y

= y + 2.y-1

It is in one variable but not polynomial because it contains (y-1) which is not a whole number.

(v) x10+y3+t50

It is a polynomial in three variables x, y and t. So, it is not a polynomial in one variable.


EX 2.1 QUESTION 2.


 Write the coefficients of x2 in each of the following:

(i) 2+x2+x

(ii) 2–x2+x3

(iii) (π/2)x2+x

(iii)√2x-1

Solution:

(i) 2 + x2 + x.
The coefficient of x2 is 1.
(ii)  2 – x2 + x3.
The coefficient of x2 is -1.
(iii)  \frac { \pi }{ 2 } { x }^{ 2 }+ x.
The coefficient of x2 is  \frac { \pi }{ 2 }.
(iv) √2 x – 1.
The coefficient of x2 is 0.


EX 2.1 QUESTION 3.


Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Solution:

(i) A binomial of degree 35 = 3x35 -4.
(ii) A monomial of degree 100 = 3x100.


EX 2.1 QUESTION 4.


Write the degree of each of the following polynomials.
(i) 5x3+4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7
(iv) 3

Solution:

(i) The degree of 5x3 + 4x2 + 7x = 3.

(ii) The degree of 4- y2 =  2.

(iii) The degree of 5t – √7 = 5t1 – √7 = 1

(iv) The degree of 3 = 3x° = 0          [∵ x°=1]