EXERCISE 2.2
Q 1, Ex 2.2, Page No 34, Polynomials, CBSE Class 9th Maths
Page No 32:
Question 1:
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) $4 x^{2}-3 x+7$
(ii) $y^{2}+\sqrt{2}$
(iii)$3 \sqrt{t}+t \sqrt{2}$
(ii) $y^{2}+\sqrt{2}$
(iii)$3 \sqrt{t}+t \sqrt{2}$
(iv) $y+\frac{2}{y}$
(v) $x^{10}+y^{3}+t^{50}$
(v) $x^{10}+y^{3}+t^{50}$
Answer:
(i) $4 x^{2}-3 x+7$
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 term $3 \sqrt{t}$ is $\frac{1}{2}$, 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 $\frac{2}{y}$ 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.
Q 2 (i), Ex 2.2, Page No 34, Polynomials, Class 9th NCERT Maths
Q 2 (ii), Ex 2.2, Page No 34, Polynomials, NCERT Solutions Class 9th
Q 2 (iii and iv), Ex 2.2, Page No 34, Polynomials, Class 9th Maths
Question 2:
Write the coefficients of 
in each of the following:
in each of the following:
(i) $2+x^{2}+x$
(ii) $2-x^{2}+x^{3}$
(ii) $2-x^{2}+x^{3}$
(iii) $\frac{\pi}{2} x^{2}+x$
(iv) $\sqrt{2} x-1$
(iv) $\sqrt{2} x-1$
Answer:
(i) $2+x^{2}+x$
In the above expression, the coefficient of $x^{2}$ is 1.
(ii) $2-x^{2}+x^{3}$
In the above expression, the coefficient of $x^{2}$ is −1.
(iii) $\frac{\pi}{2} x^{2}+x$
In the above expression, the coefficient of $x^{2}$ is$\frac{\pi}{2}$.
(iv) $\sqrt{2} x-1$ , or
$0 . x^{2}+\sqrt{2} x-1$
In the above expression, the coefficient of $x^{2}$ is 0.
Q 3 (i , ii , iii and iv), Ex 2.2, Page No 35, Polynomials, CBSE Class 9th
Q 3 (v , vi , vii and viii), Ex 2.2, Page No 35, Polynomials, Maths Class 9th
Question 3:
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer:
Degree of a polynomial is the highest power of the variable in the polynomial.
Binomial has two terms in it. Therefore, binomial of degree 35 can be written as $x^{35}+x^{34}$ .
Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x100.
Q 4 (i , ii , iii and iv), Ex 2.2, Page No 35, Polynomials, Maths Class 9th
Q 4 (v , vi and vii), Ex 2.2, Page No 35, Polynomials, Maths CBSE Class 9th
Question 4:
Write the degree of each of the following polynomials:
(i) $5 x^{3}+4 x^{2}+7 x$
(ii) $4-y^{2}$
(ii) $4-y^{2}$
(iii) $5 t-\sqrt{7}$
(iv) 3
(iv) 3
Answer:
Degree of a polynomial is the highest power of the variable in the polynomial.
(i) $5 x^{3}+4 x^{2}+7 x$
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) $4-y^{2}$
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) $5 t-\sqrt{7}$
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) 3
This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5:
Classify the following as linear, quadratic and cubic polynomial:
(i)$x^{2}+x$
(ii) $x-x^{3}$
(iii) $y+y^{2}+4$
(iv) $1+x$
(v) 3t
(ii) $x-x^{3}$
(iii) $y+y^{2}+4$
(iv) $1+x$
(v) 3t
(vi) $r^{2}$
(vii) $7 x^{3}$
(vii) $7 x^{3}$
Answer:
Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively.
(i) $x^{2}+x$ 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) $7 x^{3}$ is a cubic polynomial as its degree is 3.
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