Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
i) 4x² - 3x + 7    ii) y² + √2    iii) 3√t + t√2    iv) y + (2/y)   
v) x¹⁰ + y³ + t⁵⁰

Solution:

i) 4x² - 3x + 7

The given polynomial has one variable 'x'.

Thus, 4x² - 3x + 7 is a polynomial in one variable.

ii) y² + √2

The given polynomial has one variable 'y'.

Thus, y² + √2  is a polynomial in one variable.

iii) 3√t + t√2

3t^1/2 + t√2 is not a polynomial, since the power of the variable in the first term is 1/2 which is not a whole number.

iv) y + (2/y)

y + 2y^-1 is not a polynomial since the power of the variable in the second term is -1 which is not a whole number.

v) x¹⁰ + y³ + t⁵⁰

x¹⁰+ y³+ t⁵⁰ is not a polynomial in one variable since there are 3 variables x, y, and t.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 2

Video Solution:

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) 4x² - 3x + 7 (ii) y² + √2 (iii) 3√t + t√2 (iv) y + (2/y) (v) x¹⁰ + y³ + t⁵⁰

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.1 Question 1:

Summary:

4x²− 3x + 7 and y²+ √2 expressions are polynomials in one variable whereas, 3√t + t√2, y + 2/y, and x¹⁰ + y³ + t⁵⁰ expressions are not polynomials in one variable.

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