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anonymous
 4 years ago
For how many positive integers for k is the value of k^2  18k + 65 a positive prime number?
0, 1, 2, or 4?
anonymous
 4 years ago
For how many positive integers for k is the value of k^2  18k + 65 a positive prime number? 0, 1, 2, or 4?

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asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0see if you can factorise the expression:\[k^218k+65\]if you can then this implies it can only generate a prime number if one of the factors is equal to 1.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it factors into (x5)(x13) and how do you know that it can only generate a prime number if its 1? Oh! Any integer squared is automatically composite unless its 1. So we try 1 and 1 and we get 48 and 84 respectively. So, the answer is 0? But even if something is squared and it is composite, it could still be changed into prime by the 18 or the + 65

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well, not by the 18, but it could indirectly help the 65 make f(k) prime.

phi
 4 years ago
Best ResponseYou've already chosen the best response.2In general x*y is composite (by definition) unless x=1 and y is prime or y=1 and x is prime. for your case (with integer k>0) (k5)(k13) we ask can (k5) = 1 and (k13) be prime and vice versa for k=4, we get 1* 9 = 9 not prime k=6 1* 7 negative but the question asks for positive primes k= 12 7 * 1 neg k=14 9 * 1 not prime

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How come we want to make the xintercepts = 1? Doesnt that leave out a whole bunch of other numbers that we could try into the original equation?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the answer is 0 but i dont understand how you arrived at that

phi
 4 years ago
Best ResponseYou've already chosen the best response.2Do you agree with this statement: x*y is composite (by definition) unless x=1 and y is prime or y=1 and x is prime.

phi
 4 years ago
Best ResponseYou've already chosen the best response.2k^2  18 k + 65 = (k5)(k13)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes, because after the multiplication, that product would be divisible by both x and y

phi
 4 years ago
Best ResponseYou've already chosen the best response.2x*y is composite unless.... (k5)*(k13) is composite unless....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Unless one of those equals 1! Oh. I see now. Goodness I can be a real stonehead sometimes heheh. Thanks

phi
 4 years ago
Best ResponseYou've already chosen the best response.2I was getting nervous, cause I do not know how to say it any other way
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