# 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) x^{10} + y^{3} + t^{50}

**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) x^{10} + y^{3} + t^{50}

x^{10}+ y^{3}+ t^{50 }is not a polynomial in one variable since there are 3 variables x, y, and t.

**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:**

4x^{2}− 3x + 7 and y^{2}+ √2 expressions are polynomials in one variable whereas, 3√t + t√2, y + 2/y, and x^{10} + y^{3 }+ t^{50} expressions are not polynomials in one variable.