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Chapter 2 Polynomial Exercise 2.2




Chapter 2 Exercise 2.2

In this page we have NCERT Solutions for Class 9 Maths:Chapter 2 Polynomial for Exercise 2.2 . Hope you like them and do not forget to like , social share and comment at the end of the page.
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) 5x3 + 4x2 + 7x
(ii) 4 - y2
(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) x2 + x
(ii) x - x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x3
Solution:
(i) 2 + x2+ x is a quadratic polynomial as its degree is 2.
(ii) x - x3 is a cubic polynomial as its degree is 3.
(iii) y + y2+ 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) r2is a quadratic polynomial as its degree is 2.
(vii) 7x3is a cubic polynomial as its degree is 3.
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Reference Books for class 9 Math

Given below are the links of some of the reference books for class 9 Math.

  1. Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
  2. Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
  3. Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
  4. Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.



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