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Question

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) $$y^2+\sqrt 2$$
(iii) $$3\sqrt t+ t\sqrt 2$$
(iv) $$ y+\displaystyle\frac{2}{y}$$
(v) $$x^{10}+y^3+t^{50}$$


Solution

(i) In $$4x^{2}-3x+7$$. all the indies of $$x$$ are whole numbers. So, it is a polynomial in one variable $$x$$.

(ii) In $$y^{2}+\sqrt{2}$$ the index of $$y$$ is a whole number. So, it is a polynomial in one variable $$y$$.

(iii) In $$3\sqrt{t}+t\sqrt{2}=3t^{\frac{1}{2}}+\sqrt{2}\ t$$, here the exponent of first term is $$\dfrac{1}{2}$$, which is not whole number therefore is it not a polynomial.

(iv) In $$y+\dfrac{2}{y}=y+2y^{-1}$$, here the exponent of first term is $$-1$$, which is not whole number, therefore, is it not a polynomial.

(v) In $$x^{10}+y^{3}+t^{50}$$ is not a polynomial in one variable as three variable $$x,y$$ and $$t$$ occur in it.

Mathematics
RS Agarwal
Standard IX

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