# Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer - Mathematics

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+sqrt2

(iii) 3sqrtt+tsqrt2

(iv) y+2/y

(v) x^10+y^3+t^50

#### Solution

(i) 4x^2 - 3x + 7

Yes, this expressions ia polynomial in one variable x.

(ii) y^2+sqrt2

Yes, this expression is a polynomial in one variable y.

(iii) 3sqrtt+tsqrt2

No. It can be observed that the exponent of variable t in term 3sqrtt is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.

(iv) y+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 xy, and t. Therefore, it is not a polynomial in one variable.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 9 Mathematics Textbook
Chapter 2 Polynomials
Q 1 | Page 32