Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mayankdevnani

  • 4 months ago

Please Help me !! Its simple question though but i don't know how to solve it ??

  • This Question is Closed
  1. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    How to write \(\large \bf 6x^2+5xy-4y^2=0\) in another form or equation?

  2. Mokeira
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    basically, just factor out

  3. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Like i have to convert in this :- \[\large \bf (2x-y)(3x+4y)\] i can't judge out that how to obtain this equation ?

  4. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @cwrw238 help me!!

  5. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @SolomonZelman

  6. SolomonZelman
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well, you just did it, no ?

  7. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well this is the way i do these - you need to look at factors of the first coefficient and the last that is 6 and -4 6 could be 6 * 1 or 2 * 3 and -4 could be -4*1 or 4 * -1 , or -2 * 2 now we have to find a way to combine these factor so as to get the middle coefficient +5

  8. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    solomon, i do it many times but i don't get this equation

  9. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i draw up columns; |dw:1408387576129:dw|

  10. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i don't understand your method... @cwrw238

  11. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 4 links with 2 and -1 with +3 4 and 2 on the outside and -1 and 3 on inside giving (2x - y)( 3x + 4y) - this works for me

  12. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    totally confused... ??? @cwrw238

  13. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea -- it takes a bit of getting used to

  14. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6x^2 +5xy -4y^2=0 assume it factors rationally, multiply the first and last coeffs, and set up the solution to divide off the first term afterwards 6*4 = 24, factors of 24 that combine to 5 c since the last term is negative, we have different signs, since the middle term is positive, the largest factor is postivie (x+L/6) (x-s/6) 8 and 3 combine to form 5 sooo (x+8/6) (x-3/6) reduce the fractions and if there is any fraction left over, stick the bottom back in front (x+4/3) (x-1/2) (3x+4) (2x-1) thats how i tend to do it

  15. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i forgot the y :)

  16. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    actually therea an error in my last line in drawing it should read 4 * 2 and -1 * 3

  17. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    my BAD... i don't understand... @amistre64

  18. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its a method is all ...

  19. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    can you teach me step by step ??

  20. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its tricky i know - it needs a lot of practice

  21. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it would look just like what i just typed, but sure

  22. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    but i don't know this method yet,this is first chance to see this long method...@cwrw238 hehehe

  23. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ax^2 + bx + c setup the factor, assuming it has ratioanl roots (x /a) (x /a) and mutliply the first and last coefficients

  24. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    why its (x/a)(x/a) ?? @amistre64

  25. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ac = k, such that some pair of the factors of k combine to equal b

  26. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its not x/a there is a space left to determine the operations

  27. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1408388342676:dw|

  28. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x ___ ( )/a

  29. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im not sure why it works out like that, but i recall when i went thr the class that the hundreds of problems we did it just sort of patterned out this way

  30. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    like :- \[\large \bf \frac{x-2}{a}\]

  31. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    this is what you mean to say

  32. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not quite: at first we are just organizing the information, filling it in as we go \[(x \pm\frac{ r_1}{a})~~(x \pm\frac{ r_2}{a})\]

  33. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ohkk

  34. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if the last term is positive, then ++ or -- create a positive term if the last term is negative, then +- or -+ create a negative term

  35. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yeah..

  36. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    since the last term in negative, lets go with: \[(x \color{red}+\frac{ r_1}{a})~~(x \color{red}-\frac{ r_2}{a})\] now, when we add up to get the middle term, the sign tells us which is larger, in this case +5 means the the positive part is larger than the negative part \[(x +\frac{\color{red}L}{a})~~(x -\frac{ \color{red}s}{a})\]

  37. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    correct

  38. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, we can determine L and s in a more usual way: 6 * 4y^2 = 24y^2 the factors being: 8y,3y will combine to make 5y agreed?

  39. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    another way of writing this :- 6*(-4y^2)=-24y^2 the factors being: 8y,-3y will combine to make 5y am i correct ? @amistre64

  40. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes \[(x +\frac{\color{red}{8y}}{6})~~(x -\frac{ \color{red}{3y}}{6})\] then we simply reduce the fractions, and if any are left oever, stick the bottom back in front \[(x +\frac{{4y}}{3})~~(x -\frac{{1y}}{2})\]

  41. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    correct

  42. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ideally, we would have factored out a 6 to start with and ended up with:\[6~~(x +\frac{{4y}}{3})~~(x -\frac{{1y}}{2})\] \[3(x +\frac{{4y}}{3})~~2(x -\frac{{1y}}{2})\] \[(3x +4y)~~(2x -y)\] which is just visually putting the bottom of the fraction back in front where we got it from to start with

  43. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[ax^2 + bx + c\] \[a(x^2 + \frac{b}{a}x + \frac{c}{a})\] then finding the roots such that the factors of c/a add up to b/a gets us \[a(x+r_1)(x+r_2)\]

  44. myininaya
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    To factor ax^2+bx+c you find two factors of a*c that have product ac and sum b. It is the same way if you have something in this form: ax^2+bxy+cy^2 Find two factors of a*c that have product ac and sum b. Say b=m+n and ac=mn Then ax^2+mxy+nxy+cy^2 Now we factor by grouping... So pretend we have x^2+6xy+9y^2 ac=9 and b=6 ac=9=3(3) and b=3+3 so we have x^2+3xy+3xy+9y^2 Then factor by grouping x(x+3y)+3y(x+3y) (x+3y)(x+3y) (x+3y)^2

  45. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im using the term roots incorrectly most likely .... the factors of c/a that do this and that

  46. myininaya
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Another example: 3x^2-7xy -6y^2 Let's see if you can factor this one... what is a,b, and c? then you must find a*c. then you must find two factors of a*c such that when multiplied together you get ac and when you add them you get b. Let's do this slowly.. First question what is a,b, and c?

  47. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Sorry :( for not answering your question,but i know how to do it :- Here is method(suggest by you):- ab=-24 and a+b=5 Now,we get a=8 and b=3 So,we get \[\large \bf 6x^2+8xy-3xy-4y^2=0\] \[\large \bf 2x(3x+4y)-y(3x+4y)=0\] \[\large \bf (2x-y)(3x+4y)=0\] \(\large \bf \color{red}{Answer}\)^^^

  48. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    am i correct?

  49. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @myininaya mam

  50. myininaya
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes you are done with the factoring

  51. mayankdevnani
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 3

    THANK YOU GUYS for helping me......i appreciate your work.. @cwrw238 , @amistre64 (once again thank you so much) and mostly to you @myininaya mam....

  52. cwrw238
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yw

  53. amistre64
    • 4 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    youre welcome

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.