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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