In this page we have NCERT Solutions for Class 9 Maths:Chapter 2 Polynomial for
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class 9 maths chapter 2 exercise 2.2 solutions
Question 1:
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
i. $4x^2- 3x + 7$
ii. $y^2 + \sqrt {2}$
iii. $3 \sqrt {t} + t \sqrt { 2}$
iv. $y + \frac {2}{y}$
v. $x^{10} + y^3 + t^{50}$ Solution:
(i)$4x^2- 3x + 7$
Yes, this expression is a polynomial in one variable x.
(ii)$y^2 + \sqrt {2}$
Yes, this expression is a polynomial in one variable y.
(iii)$3 \sqrt {t} + t \sqrt { 2}$
No. It can be observed that the exponent of variable t in term3 √t is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.
(iv)$y + \frac {2}{y}$
No. It can be observed that the exponent of variable y in term 2/y is -1 which is not a whole number. Therefore, this expression is not a polynomial.
(v)$x^{10} + y^3 + t^{50}$
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.
Question 2.
Write the coefficients of $x^2$ in each of the following:
i.$2 + x^2 + x$
ii. $2 - x^2 + x^3$
iii.$(\frac {\pi}{2})x^2 + x$
iv. $ \sqrt {2} x -1$ Solution:
(i) $2 + x^2 + x$
Coefficient of $x^2$ is 1.
(ii) $2 - x^2 + x^3$
Coefficient of $x^2$ is -1.
(iii)$(\frac {\pi}{2})x^2 + x$
Coefficient of $x^2$ is (π/2)
(iv) $ \sqrt {2} x -1$
There is no term consisting of $x^2$. Therefore, coefficient of $x^2$ is 0.
Question 3
Give one example each of a binomial of degree 35, and of a monomial of degree 100. Solution:
Degree of a polynomial is the highest power of variable in the polynomial.
Binomial has two terms in it. So binomial of degree 35 can be written as $x^{35}+ 1$.
monomial has only one term in it. So monomial of degree 100 can be written as $x^{100}$.
Question 4.
Write the degree of each of the following polynomials:
(i) 5x^{3} + 4x^{2} + 7x
(ii) 4 - y^{2}
(iii) 5t -√ 7
(iv) 3 Solution:
(i)This is a polynomial in variable x and the highest power of variable x is 3 Therefore, the degree of this polynomial is 3.
(ii)This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.
(iii)This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.
(iv)This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5.
Classify the following as linear, quadratic and cubic polynomials:
(i) x^{2} + x
(ii) x - x^{3}
(iii) y + y^{2} + 4
(iv) 1 + x
(v) 3t
(vi) r^{2}
(vii) 7x^{3} Solution:
(i) 2 + x^{2}+ x is a quadratic polynomial as its degree is 2.
(ii) x - x^{3} is a cubic polynomial as its degree is 3.
(iii) y + y^{2}+ 4 is a quadratic polynomial as its degree is 2.
(iv) 1 + x is a linear polynomial as its degree is 1.
(v) 3t is a linear polynomial as its degree is 1.
(vi) r^{2}is a quadratic polynomial as its degree is 2.
(vii) 7x^{3}is a cubic polynomial as its degree is 3.
Summary
Class 9 maths chapter 2 exercise 2.2 solutions has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also Download Polynomial Exercise 2.2 as pdf
This chapter 2 has total 6 Exercise 2.1 ,2.2,2.3 ,2.4 and 2.5. This is the second exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below