Question

Write whether the following statements are true or false. Justify your answer.

(i) \( \frac{1}{\sqrt{5}} x^{\frac{1}{2}}+1 \) is a polynomial.

(ii) \( \frac{6 \sqrt{x}+x^{\frac{3}{2}}}{\sqrt{x}} \) is a polynomial, \( x \neq 0 \)

Answer 1

(i) \(\frac1{\sqrt5}x^{1/2}+1\) is not a polynomial because here rational power (not a integer) of variable is present and in a polynomial all variable terms must have non-negative integer power.

(ii) \(\frac{6\sqrt x+x^{3/2}}{\sqrt x}\) = \(\frac{6+x\sqrt x}{\sqrt x}\) = 6 + x

which is a linear polynomial.