Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Value of n such that <img alt="n^{3}-n^{2}-n+1" src="/latex-image/?n%5E%7B3%7D-n%5E%7B2%7D-n&plus;1

Value of n (n\; \epsilon \; W) such that n^{3}-n^{2}-n+1 is a prime number is
 

Option: 1

3


Option: 2

2


Option: 3

1

 


Option: 4

-1


Answers (1)

best_answer

The correct option is (2)

\begin{aligned} & n^{3}-n^{2}-n+1 \\ =& n^{2}(n-1)-1(n-1) \\ =&\left(n^{2}-1\right)(n-1) \\ =&(n+1)(n-1)(n-1) \end{aligned}

For an expression with 3 factors, 2 factors, should equl 1 or -1 for this to be a prime number

Case 1 n-1=1 \Rightarrow n=2

Number : (2+1)(2-1)(2-1)

              = 3, which is prime

So, n= 2 is a valid answer

Case 2 n-1=-1 \Rightarrow n=0

Number : (1)(-1)(-1)= 1

It is not a prime number

So, n= 2

Posted by

Devendra Khairwa

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question