need math help! calling all smarties..

Discussion in 'Community' started by springscansing, Jun 2, 2003.

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  1. macrumors 6502a

    springscansing

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    #1
    Hey there. Studying to retake the SAT. Got a 1400 the first time, shooting for 1550+ this time.

    Need some help on this question:

    If n > 0 and 4x^2 + kx + 25 = (2x + n)^2 for all x, what is the value of k + n?

    The explaination in the book begins with:

    "We know n is positive and equals 25 when squared..."

    What I want to know is.. how the heck do they know that? How can you deduce that n = 25 when squared, hence, n = 5?

    If anyone could explain that to me I'd be very grateful. Thanks.
     
  2. macrumors 603

    shadowfax

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    #2
    4x^2 + kx + 25 = (2x + n)^2
    4x^2 + kx + 25 = 4x^2+4nx + n^2

    we assume, then, that they all correspond, and thus 4nx = kx and n^2 = 25. that is my best guess this late at night and a week after i have done any math. is the answer then 25?

    [edited because i am ****ty at expanding polynomials]
     
  3. macrumors 604

    MacBandit

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    #3
    Woo hoo long time since I've seen a problem like that. It's good though since for some reason it almost makes since just looking at it. That bodes well for when I have to retake a few math classes when I go back to school.

    Well since k and n are the odd variable that can't be factored out you are obviously going to have to work the problem out for them separatley and they recombine them once you have it simplified.

    Wish I could be more help but like I said it's been years and years even though I really like math. I'm glad I had the opportunity to even think about this though.
     
  4. arn
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    arn

    Staff Member

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    #4
    Re: need math help! calling all smarties..

    Now, it's been a long time since I've done this....

    (2x+n)^2 equals

    4x^2 + 4nx + n^2

    right? so... replace it above:

    4x^2 + kx + 25 = 4x^2 + 4nx + n^2

    so that means. k= 4n and 25=n^2

    [edit: damnit, wasn't quick enough :) though I get k+n = 25 -- but I may be wrong, I haven't done this in quite some time ]

    arn
     
  5. macrumors 604

    MacBandit

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    #5
    Re: Re: need math help! calling all smarties..

    I just worked through all of your work and I would have to agree. No problems here.

    [edit]
    Just as a side note in reworking this myself I'm not remembering how to get rid of the extra 'n' in '4nx'.[/edit]
     
  6. macrumors 603

    shadowfax

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    #6
    Re: Re: need math help! calling all smarties..

    well, with that extra time, you managed to not do anything wrong like i did. bah! :)
     
  7. thread starter macrumors 6502a

    springscansing

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    #7
    Yes, I can get to this part:

    4x^2 + kx + 25 = 4x^2 + 4nx + n^2

    But now I don't get how you know n = 5.
    If k and x both = 0, then you have:

    0 + 0 + 25 = 0 + 0 + ...

    Oh. So I guess x^2 does = 25.

    But then, the book also says k + x = 25.

    I just set x to zero, and the problem seems true with k as zero as well. Why does k + x have to be 25?
     
  8. thread starter macrumors 6502a

    springscansing

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    #8
    Actually that's really embarrasing that I just asked that, nevermind, haha.

    I get it now. Shouldn't do math at 3AM I guess.

    Thanks for the help you two!
     
  9. macrumors 603

    shadowfax

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    #9
    if it says that out of context, they're STUPID. it says "for all x."

    k + x = 25 when k = 20 cannot be true for all x. it can only be true for x = 5.

    [edit] did you mix up x^2 and n^2 up there? you said x^2=25, but this is only true for x=5. x can be anything. it's n that has to be 5 for this problem to work for all positive values of x.[/edit]
     
  10. thread starter macrumors 6502a

    springscansing

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    #10
    4x^2 + kx + 25 = 4x^2 + 4nx + n^2

    hm.. maybe. let's see
    *sets x to 1*

    4 + k + 25 = 4 + 4n + n^2

    using n as 5 since it just HAS to be 5...

    4 + k + 25 = 4 + 20 + 25
    k + 29 = 49
    k = 28

    x + k = 29

    Hm. Either I botched basic math or... something is up with this question.
     
  11. thread starter macrumors 6502a

    springscansing

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    #11
    Yes I did. I meant n = 5. Sorry. :)
     
  12. thread starter macrumors 6502a

    springscansing

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    #12
    [see above]

    Nevermind.. it's k + n that is 25, not k + x.

    *rubs eyes*

    It's okie. It's all okie.
     
  13. macrumors 603

    shadowfax

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    #13
    4x^2 + kx + 25 = 4x^2 + 4nx + n^2

    4n = k
    n^2 =25
    n = 5
    k = 20

    for x = 0:
    0 + 0 + 25 = 0 + 0 + 25
    for x = 1:
    4 + 20 + 25 = 4 + 20 + 25
    for x = 2
    16 + 40 + 25 = 16 + 40 + 25

    [edit] sorry didn't catch your revelation.

    but as a sort of recap on the SAT objective here, i think they want you to consider

    ax^2 + bx + c = dx^2 + ex + f

    where a corresponds to d, b to e, and c to f. they tried to hide it from you by leaving (2x+n)^2 un-expanded, as expanding it is the major part of the problem. but once you do, they expect you to quickly see that each term corresponds, as, from the first term, there is no n or k, and 4x^2 simply must equal 4x^2, reflexively.

    anyways, good luck to you on the SAT [/edit]
     
  14. thread starter macrumors 6502a

    springscansing

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    #14
    *salutes* thanks shadowgirl!
     
  15. macrumors newbie

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    #15
    Basic concept

    Hey, springscansing, I don't mean to hit you over the head if you already know this by heart after studying so much for the SAT, but the basic concept that this problem is conveying (and that will surely reappear on the real thing) is that on each side of the equation, the like values can always be equated. That is, all the x^2's on one side of the equation will always equal all (and only all) the x^2's on the other side of the equation, so with the x's and the constants. It actually makes solving problems like this pretty straightforward, given you've done the proper expansion. Thus for any problem like this you should always get three new, easily solved equations. In this case:

    4x^2 = 4x^2
    kx = 4nx
    25 = n^2

    Good luck on the SAT. Mine went up approximately that amount when I retook it the second time -- stupid me thought I could stay up till 4 in the morning the night before the first test! Get ahold of me next fall if you need tips applying to top colleges. Blessings.
     
  16. macrumors 603

    shadowfax

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    #16
    you're welcome, but once again, i am a guy. think of my 'tar as something like macBandit's past 'tars, or edesignuk's, featuring american-standard big-breasted women, usually focusing on that area of the body. i just don't emphasize cup size/voluptuousness in my 'tar choice. regardless, i am a male, with all the functionality that comes with being so, and would appreciate it if you used the according pronouns and other such nouns. thanks!
     
  17. thread starter macrumors 6502a

    springscansing

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    #17
    ...

    I really thought you were a girl.

    Who's next to reveal to me they are really a man... vinow?!
     
  18. macrumors 603

    shadowfax

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    #18
    oh. well i tried to tell you once before when we were duking it out in another thread. i guess you thought i was joking. good to have that figured out :)

    jeez, though, springs, you ask a simple question and get insulted by 3 people saying the same thing to you over and over. sorry. for my part, i didn't say much of anything after anyone else :D

    1400 is a good first score, especially if you didn't prepare much. i got a 1430 the first time i took the SAT, and decided not to bother doing it again, since i didn't think i would need to. i know a lot of people that took it 2-3 times, and the ones that did work in between usually improved by 70-100 points or so. but 1550 is very doable with a bit of studying. good luck man.
     
  19. thread starter macrumors 6502a

    springscansing

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    #19
    Yeah I didn't prepare the first time. Or take the PSATs.

    I was taking the SAT and I was like hold on, so one section doesn't count? lol

    So yeah I should be able to get 1550.

    And about the insults, don't worry, I get it wherever I go. People take me the wrong way... a lot. Even in person. It's magnified heavily online though I suppose. I often come off as some totally deraged arrogant freak when really I'm only slightly deranged and just have a healthy self image...

    See that was a joke.

    Kinda.
     
  20. thread starter macrumors 6502a

    springscansing

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    #20
    Btw, I'm actually a girl myself. Lots of people don't know that.

    Here's me:
     
  21. macrumors 603

    shadowfax

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    #21
    it's about time to make a link to the nude pics, i think :D :D :D
     
  22. thread starter macrumors 6502a

    springscansing

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    #22
    :eek:

    You'll get no naked pictures of me!
     
  23. macrumors regular

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    Mar 7, 2003
    #23
    1550 shouldn't be a problem if you got 1400 first time w/o studying.

    Few simple suggestions:
    1. Look for simplifications, cancellations, multiply by f(x)/f(x) = 1, etc. This also goes for systems of equations.
    2. If you can't find such shortcuts within 15 seconds, expand everything.
    3. The "like terms" thing mentioned above.
    4. Drink coffee/caffeinated-something (I prefer Frappuccino) and eat something sweet before taking the test, but not right before. Energy boost.

    P.S. - You're quite attractive. (really)
     
  24. macrumors 604

    scem0

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    #24
    no, the girl in the picture is attractive. :rolleyes: ;)
     
  25. macrumors 65816

    mrjamin

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    #25
    not sure we want any going from your 'tar - especially seeing as you're a bloke :D
     
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