A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Help MEDAL GIVEN !!!

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The roots of the equation \[2x^2 + 5x - 8 = 0\] are \[\alpha \] and \[\beta \]. Find the quadratic equations whose roots are : \[5\alpha + \frac{ 1 }{ \alpha }, 5\beta + \frac{ 1 }{ \beta } \]

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

    @robtobey

  3. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Have you found the sum and product of them?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no

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

    I did this :

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

    \[\alpha+\beta = \frac{ -5 }{ 2 } \] , \[\alpha \beta = \frac{ -8 }{ 2 } = -4\] New sum = \[5\alpha + \frac{ 1 }{ \alpha } + 5\beta + \frac{ 1 }{ \beta } \] I don't know what to do now

  7. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    well why not make it \[\frac{5\alpha^2 + 1}{\alpha} + \frac{5\beta^2 + 1}{\beta}\]

  8. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then you take the sum and product of that?

  9. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    then get the common denominator and add the numerators

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

    then for new product: \[(5\alpha + \frac{ 1 }{ \alpha })* (5\beta+\frac{ 1 }{ \beta })\] in the end I got the answer to be : \[8x^2 -95 - 786\]. which I believe is wrong :( !!!

  11. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then input the sum and product into \(\sf x^2 -(\text{sum of roots})x +(\text{product of roots})=0\)?

  12. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    look at the sum of the roots this way \[5\alpha + 5 \beta = \frac{1}{\alpha} + \frac{1}{\beta} = 5(\alpha + \beta) + \frac{\alpha + \beta}{\alpha \beta}\] does that help

  13. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    oops should read \[5 \alpha + 5 \beta + \frac{1}{\alpha} + \frac{1}{\beta}\]

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

    ahh yes that does help very much .. cheers :)

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so was I correct then ????

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what did you guys get as your final answer???

  17. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    5(-5/2) + (-5/2)/-4 = -100/8 + 5/8 = -95/8 so that seems correct

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what about the product ... it seems way tooo big

  19. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    as for the product I thought \[(5\alpha + \frac{1}{\alpha})(5\beta + \frac{1}{\beta} = 25\alpha \beta + \frac{5\alpha}{\beta} + \frac{5\beta}{\alpha} + \frac{1}{\alpha \beta}\]

  20. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    which becomes \[25 \alpha \beta + \frac{5 \alpha^2 + 5\beta^2}{\alpha \beta} + \frac{1}{\alpha \beta}\] or \[25 \alpha \beta + \frac{5[(\alpha + \beta)^2 - 2 \alpha \beta]}{\alpha \beta} + \frac{1}{\alpha \beta}\]

  21. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so I think you need to be careful with the signs

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tooo confusing wht do you get as finl answer ???

  23. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i got -4

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok ....

  25. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so if -b/a = -95/8 then c/a = -32/8 so a = 8, b = 95 and c -32 that's my best guess

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I got something else

  27. 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.