King
  • King
:Help...........for how many positive integers n is n^3 -8n^2+20n-13 a prime number??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
factorize it
King
  • King
how watever i get is not a prime number
King
  • King
why?

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King
  • King
oh
King
  • King
but then ii have to plug in millions of values
anonymous
  • anonymous
what u want to calculate
anonymous
  • anonymous
(n^3 -8n^2+20n-13) a prime number
anonymous
  • anonymous
or n is a prime number
King
  • King
for n i will have to put millions of values to find how may n positive integers satisfy n^3 -8n^2+20n-13 to be a prime number
anonymous
  • anonymous
ok
King
  • King
so,what to do??
King
  • King
anything i can do to narrow down the possobilities
King
  • King
no answer given....
anonymous
  • anonymous
ok see for 2 it is prime number
anonymous
  • anonymous
wait i took wrong concept
anonymous
  • anonymous
\[(x-1) \times [(x-7)x + 13]\]
anonymous
  • anonymous
where x is n
King
  • King
ok
anonymous
  • anonymous
now see the first term is (x-1). and other than 2 no other even number is a prime number right
anonymous
  • anonymous
i got the answer
King
  • King
no n does not have to be a prime number n^3 -8n^2+20n-13 has to be a prime number
anonymous
  • anonymous
yeah i know (x−1)×[(x−7)x+13] it has to be prime
King
  • King
yup so x can be anything greater or equal to 2
anonymous
  • anonymous
first term is (x-1) and two is the only even prime number.
anonymous
  • anonymous
but if u will subtract 1 from any other prime number the resultant will be divisible by 2
anonymous
  • anonymous
getting my point or not
King
  • King
x can be 4
anonymous
  • anonymous
yeah u r right
anonymous
  • anonymous
it means that for any odd integer other than 3 u will not get a prime number
King
  • King
yeah
anonymous
  • anonymous
Superb sheggy!
anonymous
  • anonymous
also the number cannot be graeter than 7
King
  • King
oh yeah
anonymous
  • anonymous
thanks fool bhai
anonymous
  • anonymous
so u are having a limited space to work out that is from 1 to 7
King
  • King
yes sheg u got it so answer is n=2,3,4
King
  • King
no actually 2 to 7
anonymous
  • anonymous
hahahaa right 2 to 7
anonymous
  • anonymous
but for 7 it will be 0
King
  • King
wait why cant it be greater than 7?
anonymous
  • anonymous
try any number u will get the answer
anonymous
  • anonymous
odd numbers cannot be included ok thats true
anonymous
  • anonymous
as i had told u any odd number subtracted by one will result in even number so it will be divisible by 2.........do u accept it or not
King
  • King
is 323 a prime number?
King
  • King
yeah i acept
King
  • King
its not div by 17
anonymous
  • anonymous
323 is divisible by 17
anonymous
  • anonymous
so 323 is not a prime number
King
  • King
4387 ?
anonymous
  • anonymous
what u have put x = ??
King
  • King
n=20
King
  • King
1443?
King
  • King
gtg shall come bak in 15 min
anonymous
  • anonymous
for n = 20 it should be equal to 5187
King
  • King
oh yeah 1443?
King
  • King
no
anonymous
  • anonymous
20^3 - 8*20^2 + 20*20 -13 =8000 - 3200 + 400 -13 = 8400 - 3213 = 5187
King
  • King
gtg cum bak in 15 mins
anonymous
  • anonymous
dear i had told u for no value greater than 7 it would fit
anonymous
  • anonymous
and both 1443 and 5187 is divisible by 3
King
  • King
i am bak so what to do now?
anonymous
  • anonymous
for no value greater than 7 that too even number it will not be a prime number
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=x^3-8x^2%2B20x-13+where+x+%3D+20 visit this website and plug in different value of x u will get the answer
anonymous
  • anonymous
king u there

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