A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

One of the roots of the equation x^2+Kx−6=0 is 3 and K is a constant. Which one is greater a. The value of K b. -1

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

    one of the roots is 3 that means x=3 or , adding -3 to both sides, x-3=0 let the other root be called "a" then we know (x-3)(x-a)=0 multiply that out x^2 -3x-ax +3a = 0 or x^2 -(3+a) x + 3a =0

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

    match up x^2 -(3+a) x + 3a =0 x^2+Kx−6=0 we see 3a= -6 solve for a by dividing both sides by 3 we get a= -2

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

    using a= -2 in x^2 -(3+a) x + 3a =0 x^2 -(3-2) x +3*-2 = 0 simplifying: x^2 - (1) x -6 =0 or x^2 -x -6 =0

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

    it looks like K= -1

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

    why is one of the roots 3?

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

    It says One of the roots of the equation x^2+Kx−6=0 is 3

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

    Hey how do i know if it's (x-3)(x-a) and not (x+a) ?????????

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

    I tried (x-3)(+a) and it worked out better

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

    (x+a)*

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

    say you factored a quadratic and got (x-3)(x-2) = 0 the roots are the x values that make this expression zero. this will be zero if x=3 (which makes 3-3 zero) or x=2 (which makes 2-2 zero) if you had (x-3) (x+2)=0 the second root is when x= -2 notice if we write (x+2) as (x - (-2)) the number -2 is the root. in other words, if we write (x-a) then a will be the root (the x value that makes the expression zero)

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

    btw, what is question ? It looks like it was cut off at the top.

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

    It's asking which one is greater a or b

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

    so in what cases would it be (x-3) (x+a)

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

    in this case , K = -1, so they are equal

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

    I'm still having a hard time understanding how I would know for sure that it would be (-)(-) instead of (-)(+) or (+)(-)

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

    Let's factor x^2 -x -6 =0 the -6 means 1) different signs on the roots, 2) they multiply to give us 6 1,6 2,3 are the choices the -1x means the larger nuumber is negative, and they add to -1 so 2 and -3 are the factors (x+2)(x-3)=0 or (x - (-2)) (x-3) = 0

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

    I guess the point is you can always write the factors as (x - a) where a is the root. if the root were -2 x= -2 makes the expression zero, then the factor would be (x- -2) (which is the same as (x+2) )

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

    But I think I am being a clear as mud here.

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

    lolol

  20. 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.