If $x^{g}$ + $\frac{1}{x^{a}}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial?

___

Open in App

Solution

$x^{g}$ + $\frac{1}{x^{a}} = x^{g} + x^{- a}$
Since g = a
$x^{g} + \frac{1}{x^{a}} = x^{a} + x^{- a}$
For the expression $x^{a} + x^{- a}$ to be a polynomial, a and -a must be whole numbers.
Thus, a = 0

Suggest Corrections

Similar questions

If $x^{a}$ + $\frac{1}{x^{b}}$ is a polynomial in one variable and if it is given that $a = b$ , then this is a polynomial for $a =$ ___

If $x^{g} + \frac{1}{x^{a}}$ is a polynomial in one variable, what could be the value of $^{'} a^{'}$ ?

If $x^{g} + \frac{1}{x^{a}}$ is a polynomial in one variable, What could be the value of $a$ ?

If $x^{g} + \frac{1}{x^{a}}$ is a polynomial, what could be the value of $a$ ?

Join BYJU'S Learning Program