Question :-
+ x + 11 is a prime number. Which of the following is invalid value of x?
a) 8
b) 5
c) 12
d) 10
Please give Answer with explanations !!
Answers
Answer:
10
Step-by-step explanation:
10 is right ans because after putting in equation value of x = 10
10²+10+11 = 121 that's not be prime number so,
10 is right ans
Answer:
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⇝8
2
+8+11
\sf \leadsto 64 + 8 + 11⇝64+8+11
\sf \leadsto 83⇝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⇝5
2
+5+11
\sf \leadsto 25 + 5 + 11⇝25+5+11
\sf \leadsto 41⇝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⇝12
2
+12+11
\sf \leadsto 144 + 12 + 11⇝144+12+11
\sf \leadsto 167⇝167
→ Here , 167 is a prime number . So , it is not the invalid option .
_________
★ Option ( d ) ' 10 ' ★
\sf \leadsto 10^{2} + 10 + 11⇝10
2
+10+11
\sf \leadsto 100 + 10 + 11⇝100+10+11
\sf \leadsto 121⇝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 )