A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 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?

  • This Question is Closed
  1. asnaseer
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    see if you can factorise the expression:\[k^2-18k+65\]if you can then this implies it can only generate a prime number if one of the factors is equal to 1.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it factors into (x-5)(x-13) 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

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, not by the -18, but it could indirectly help the 65 make f(k) prime.

  4. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    In 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) (k-5)(k-13) we ask can (k-5) = 1 and (k-13) 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

  5. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It looks like zero primes

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How come we want to make the x-intercepts = 1? Doesnt that leave out a whole bunch of other numbers that we could try into the original equation?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer is 0 but i dont understand how you arrived at that

  8. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Do 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.

  9. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    k^2 - 18 k + 65 = (k-5)(k-13)

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, because after the multiplication, that product would be divisible by both x and y

  11. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so x=(k-5) and y= (k-13)

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  13. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    x*y is composite unless.... (k-5)*(k-13) is composite unless....

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Unless one of those equals 1! Oh. I see now. Goodness I can be a real stonehead sometimes heheh. Thanks

  15. phi
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I was getting nervous, cause I do not know how to say it any other way

  16. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.