NCERT Solutions Class 9 Mathematics

Exercise 2.1

Q.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 + $\sqrt{2}$ (iii) 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$

(iv) y + $\frac{2}{\mathrm{y}}$ (v) x10 + y3 + t50

Q.2: Write the coefficients of x2 in each of the following:

1. 2 + x2 + x

2. 2 - x2 + x3

3. $\frac{\mathrm{\pi }}{2}$ x2 + x

4. $\sqrt{2}$x - 1

Q.3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Q.4: Write the degree of each of the following polynomials:

1. 5x3 + 4x2 + 7x

2. 4 - y2

3. 5t - $\sqrt{7}$

4. 3

Q.5: Classify the following as linear, quadratic and cubic polynomial:

 x2 + x x - x3 y + y2 +4 1 + x t r2 7x3

NCERT Solutions Class 9 Mathematics

Exercise 2.1

Q.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 + $\sqrt{2}$ (iii) 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$

(iv) y + $\frac{2}{\mathrm{y}}$ (v) x10 + y3 + t50

Solution:

1. 4x2 - 3x + 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable.

2. y2 + $\sqrt{2}$: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.

3. 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$: This is an expression with only one variable t but one of the powers of t is $\frac{1}{2}$ (in 3$\sqrt{\mathrm{t}}$), which is not +ve integer. Hence, this is not a polynomial.

4. y + $\frac{2}{\mathrm{y}}$ = y + 2y-1: This is an expression with only one variable y but one of the powers of y is -1, which is not +ve integer. Hence, this is not a polynomial.

5. x10 + y3 + t50:There are three variable x, y and t, hence, this is not a polynomial in one variable.

6. Q.2: Write the coefficients of x2 in each of the following:

1. 2 + x2 + x

2. 2 - x2 + x3

3. $\frac{\mathrm{\pi }}{2}$ x2 + x

4. $\sqrt{2}$x - 1

Solution:

1. 2 + x2 + x: coefficients of x2 = 1

2. 2 - x2 + x3: coefficients of x2 = -1

3. $\frac{\mathrm{\pi }}{2}$ x2 + x: coefficients of x2 = $\frac{\mathrm{\pi }}{2}$

4. $\sqrt{2}$x - 1: coefficients of x2 = 0

Q.3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Solution:

Binomial of degree 35: 4x35+7

Monomial of degree 100: 3x100

Q.4: Write the degree of each of the following polynomials:

1. 5x3 + 4x2 + 7x

2. 4 - y2

3. 5t - $\sqrt{7}$

4. 3

Solution:

1. 5x3 + 4x2 + 7x : degree 3

2. 4 - y2 : degree 2

3. 5t - $\sqrt{7}$ : degree 1

4. 3 : degree 0.

Q.5: Classify the following as linear, quadratic and cubic polynomial:

 x2 + x x - x3 y + y2 +4 1 + x t r2 7x3

Solution:

 x2 + x: Quadratic Polynomial x - x3: Cubic Polynomial y + y2 +4: Quadratic Polynomial 1 + x: Linear Polynomial 3t: Linear Polynomial r2: Quadratic Polynomial 7x3: Cubic Polynomial