Question

Question :-
$\sf{{x}^{2}}$+x+11 is a prime number. Which one of the following is invalid value of x?

Options :-
a) 8
b) 5
c) 12
d) 10 ​

Answer 1

Given :-

• x² + x + 11 is a prime number

To Find :-

• Invalid value of x from the given options

Solution :-

→ Let's solve putting the value of ' x ' in every option to find the invalid value .

★ Option ( a ) ' 8 ' ★

→ Let's put the value of ' x ' as 8

$\sf \leadsto 8^{2} + 8 + 11$

$\sf \leadsto 64 + 8 + 11$

$\sf \leadsto 83$

→ Here , 83 is a prime number . So, it is not the invalid option .

_________

★ Option ( b ) ' 5 ' ★

→ Let's put the value of ' x ' as 5

$\sf \leadsto 5^{2} + 5 + 11$

$\sf \leadsto 25 + 5 + 11$

$\sf \leadsto 41$

→ Here , 41 is a prime number . So , it is not the invalid option .

__________

★ Option ( c ) ' 12 ' ★

→ Let's put the value of ' x ' as 12

$\sf \leadsto 12^{2} + 12 + 11$

$\sf \leadsto 144 + 12 + 11$

$\sf \leadsto 167$

→ Here , 167 is a prime number . So , it is not the invalid option .

_________

★ Option ( d ) ' 10 ' ★

$\sf \leadsto 10^{2} + 10 + 11$

$\sf \leadsto 100 + 10 + 11$

$\sf \leadsto 121$

→ Here , 121 is not a prime number as it is divisible by 11 . So , it is the invalid option .

∴ 10 is the value which is invalid for x² + x + 11 = Prime no.

  ( Option d )