Make the correct alternative in following question:

Question:

Make the correct alternative in following question:

If $x^{n}-1$ is divisible by $x-\lambda$, then the least positive integral value of $\lambda$ is

(a) 1                    

(b) 2                    

(c) 3                    

(d) 4

Solution:

Let $\mathrm{P}(n): x^{n}-1$ is divisible by $(x-\lambda)$.

As, for $n=1$,

$\mathrm{P}(1)=x^{1}-1=x-1$

As, $\mathrm{P}(1)$ must be divisible by $(x-\lambda)$.

$\Rightarrow(x-1)$ must be divisible by $(x-\lambda)$.

So, $\lambda=1$

Hence, the correct alternative is option (a).

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