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  4. The set A= x: x4-x3-x2=0. and .x ∈ N represent a ...X... . Here, X refers to

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Q. The set $A=\left\{x: x^4-x^3-x^2=0\right.$ and $\left.x \in N\right\}$ represent a ...X... . Here, $X$ refers to

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Solution:

Given equation can be written as
$\Rightarrow x^2\left(x^2-x-1\right) =0$
$\Rightarrow x =0, \frac{1 \pm \sqrt{5}}{2}$
$\therefore$ There is no natural value of $x$ which satisfies $x^4-x^3-x^2=0$