Our ncert solutions for Exercise 2.1 Class 9 maths 2. Polynomials - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.
Exercise 2.1 Class 9 maths 2. Polynomials - ncert solutions - Toppers Study
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Exercise 2.1 Class 9 maths 2. Polynomials - ncert solutions - Toppers Study
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Exercise 2.1 class 9 Mathematics Chapter 2. Polynomials
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2. Polynomials
| Exercise 2.1 |
Exercise 2.1 Class 9 maths 2. Polynomials - ncert solutions - Toppers Study
Exercise 2.1
Q1. 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
It is polynomial in one variable. Because the power of variable is natural number.
(ii) y2 + √2
It is polynomial in one variable. Because the power of variable is natural number.
(iii)3√t + t√2
It is not a polynomial in one variable. Because the power of variable is not a natural number, it is a fractional number.
(iv) y +2/y
It is not a polynomial in one variable.
(v) x10 + y3 + t50
It is not a polynomial in one variable. while It is a polynomial in three variable.
Q2. Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x
(ii) 2 – x2 + x3 (
iii) π/2 x2 + x
(iv) √2x −1
Solution:
(i) 2 + x2 + x
Coefficient of x2 = 1
(ii) 2 – x2 + x3
Coefficient of x2 = –1
(iii) π/2 x2 + x
Coefficient of x2 = π/2
(iv) √2x −1
Coefficients of x2 = 0 [Because There is no x2 So coefficient will be 0]
Q3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
A binomial of degree 35
⇒ 2x35 + 5y
Note: Binomial means the expression of two terms. Like x + 5, 3a - 2b, 3t + 7 etc.
A monomial of degree 100
⇒ 3y100
Note: Monomial means the expression of single term, like 3x, 5t, y, 3xy etc.
Q4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7
(iv) 3
Solution:
(i) 5x3 + 4x2 + 7x
Ans: The degree of polynomial = 3 [Highest power]
(ii) 4 – y2
Ans: The degree of polynomial = 2
(iii) 5t – √7
Ans: The degree of polynomial = 1
(iv) 3
Ans: The degree of polynomial = 0
[Note: There is no variable therefore degree = 0]
Q5. Classify the following as linear, quadratic and cubic polynomials:
(i) x2 + x
(ii) x – x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x2
Solution:
(i) x2 + x
Ans: Quadratic polynomial
(ii) x – x3
Ans: Cubic polynomial
(iii) y + y2 + 4
Ans: Quadratic polynomial
(iv) 1 + x
Ans : Linear polynomial
(v) 3t
Ans : Linear polynomial
(vi) r2
Ans: Quadratic polynomial
(vii) 7x2
Ans: Cubic polynomial
Other Pages of this Chapter: 2. Polynomials
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