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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