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

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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`

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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.

Concept: Polynomials in One Variable
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APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Q 1 | Page 32

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