Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jvaldez45 Group Title

If a is uniformly distributed over [−28,28], what is the probability that the roots of the equation x2+ax+a+80=0

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    what is the probability that the roots of the equation what?

    • 2 years ago
  2. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    what it the probability that the roots of the equation are real?

    • 2 years ago
  3. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    are both real?

    • 2 years ago
  4. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    oh ok we can solve that using the quadratic formula

    • 2 years ago
  5. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

    • 2 years ago
  6. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what would be the b value of the equation. is it a(x+1)

    • 2 years ago
  7. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[x^2+ax+a+80=0 \] \[x=\frac{-a\pm\sqrt{a^2-4a-320}}{2}\]

    • 2 years ago
  8. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    no if you use the quadratic formula, \(a=1,b=a, c=a+80\) different \(a\) of course

    • 2 years ago
  9. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    if these are to be real numbers, that means you must have \[a^2-4a-300\geq 0\]

    • 2 years ago
  10. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get that?

    • 2 years ago
  11. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    by some miracle this factors as \[(a-20)(a+16)\geq 0\] so we can actually solve

    • 2 years ago
  12. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    how did i get \(a^2-4a-320\)?

    • 2 years ago
  13. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • 2 years ago
  14. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    or how did i get the whole equation?

    • 2 years ago
  15. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get that? the stuff under the square root has to be 0 or positive, else you get imaginary numbers when you take the root.

    • 2 years ago
  16. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks

    • 2 years ago
  17. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ok quadratic formula tells you the solution to \(ax^2+bx+c=0\) is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) in your case \(a=1,b=a,c=a+80\)

    • 2 years ago
  18. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    when you compute you get \[x=\frac{-a\pm\sqrt{a^2-4a-320}}{2}\] in your case so for these to be real, the discriminant \(a^2-4a-320\) must be greater than or equal to zero, otherwise you have a negative number under the radical

    • 2 years ago
  19. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    oh, what @phi said

    • 2 years ago
  20. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so after i find my values what do I do?

    • 2 years ago
  21. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    your last job is to solve for \(a\) \[a^2-4a-320\geq 0\]

    • 2 years ago
  22. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i found my values and they are a=20 and a+-16

    • 2 years ago
  23. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    this factors as \((a-20)(a+16)\geq 0\)

    • 2 years ago
  24. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    a=-16

    • 2 years ago
  25. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    hold on, you are not solving \((a-20)(a+16)=0\) but rather \[(a-20)(a+16)\geq 0\]

    • 2 years ago
  26. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    the zeros are \(-16\) and \(20\) for sure but you want to know the interval over which it is positive since this is a quadratic with leading coeffient positive, it will be positive outside the zeros, in other words if \(a\leq -16\) or \(a\geq 20\)

    • 2 years ago
  27. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    your final job is to find what portion of the interval \([-28,28]\) satisfies \(a\leq -16\) or \(a\geq 20\)

    • 2 years ago
  28. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so i would have to find the interval of the it by integrating it?

    • 2 years ago
  29. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    not necessary, just look

    • 2 years ago
  30. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    favorable part is \([-28,-16]\cup [20,28]\)

    • 2 years ago
  31. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    you can eyeball the total length

    • 2 years ago
  32. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    12 and 8

    • 2 years ago
  33. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    right, for a total of 20

    • 2 years ago
  34. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks just found the answer. thank you

    • 2 years ago
  35. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yw

    • 2 years ago
  36. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    hope it was \(\frac{20}{56}\)

    • 2 years ago
  37. jvaldez45 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yea

    • 2 years ago
    • Attachments:

See more questions >>>

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.