Polynomials
Exercise 2.1 Part 1
Question 1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) `4x^2 -3x + 7`
Answer: Since, the given expression has only one variable ‘x’, hence this is a polynomial in one variable.
(ii) `y^2 + sqrt2`
Answer: Since, the given expression has only one variable ‘y’, hence this is a polynomial in one variable.
(iii) `3sqrt\t + t\sqrt2`
Answer: Since, variable, ‘t’ in this expression exponent of variable is not a whole number. [Exponent of a variable in a polynomial must be a whole number. Expression with exponent of a variable in fraction is not considered as a polynomial.]
(iv) `y + 2/y`
Answer: Since, exponent of the variable is negative integer, and not a whole number, hence it cannot be considered a polynomial.
(v) `x^10 + y^3 + t^50`
Answer: Since, given expression has three variables, i.e. x, y and t, so it is not a polynomial in one variable.
Question 2: Write the coefficients of x2 in each of the following:
(i) `2 + x^2 + x`
Answer: Given; `2 + x^2 + x`
Here, coefficient of `x^2 = 1`
(ii) `2 – x^2 + x^3`
Answer: Here, coefficient of `x^2 = 1`
(iii) `(π)/(2)\x^2 + x`
Answer: Here, coefficient of `x^2 = π/2`
(iv) `sqrt2x – 1`
Answer: Here, coefficient of `x^2 = 0`