View Full Version : need math help! calling all smarties..

springscansing

Jun 3, 2003, 01:42 AM

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.

shadowfax

Jun 3, 2003, 01:47 AM

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]

MacBandit

Jun 3, 2003, 01:49 AM

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.

Originally posted by springscansing

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.

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

MacBandit

Jun 3, 2003, 01:52 AM

Originally posted by arn

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 ]

arn

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

Just as a side note in reworking this myself I'm not remembering how to get rid of the extra 'n' in '4nx'.

shadowfax

Jun 3, 2003, 01:56 AM

Originally posted by arn

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 well, with that extra time, you managed to not do anything wrong like i did. bah! :)

springscansing

Jun 3, 2003, 01:56 AM

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?

springscansing

Jun 3, 2003, 01:58 AM

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!

shadowfax

Jun 3, 2003, 02:00 AM

Originally posted by springscansing

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? 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.

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.

springscansing

Jun 3, 2003, 02:08 AM

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.

springscansing

Jun 3, 2003, 02:10 AM

Originally posted by Shadowfax

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. [/B]

Yes I did. I meant n = 5. Sorry. :-)

springscansing

Jun 3, 2003, 02:12 AM

[see above]

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

*rubs eyes*

It's okie. It's all okie.

shadowfax

Jun 3, 2003, 02:15 AM

Originally posted by springscansing

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. 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

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

springscansing

Jun 3, 2003, 02:32 AM

*salutes* thanks shadowgirl!

Ajohn

Jun 3, 2003, 02:41 AM

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.

shadowfax

Jun 3, 2003, 02:43 AM

Originally posted by springscansing

*salutes* thanks shadowgirl! 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!

springscansing

Jun 3, 2003, 02:45 AM

...

I really thought you were a girl.

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

shadowfax

Jun 3, 2003, 02:56 AM

Originally posted by springscansing

...

I really thought you were a girl.

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

springscansing

Jun 3, 2003, 03:04 AM

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.

springscansing

Jun 3, 2003, 03:07 AM

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

Here's me:

shadowfax

Jun 3, 2003, 03:12 AM

it's about time to make a link to the nude pics, i think :D :D :D

springscansing

Jun 3, 2003, 03:14 AM

:eek:

You'll get no naked pictures of me!

iMook

Jun 3, 2003, 08:04 AM

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)

scem0

Jun 3, 2003, 08:07 AM

no, the girl in the picture is attractive. :rolleyes: ;)

mrjamin

Jun 3, 2003, 10:27 AM

Originally posted by springscansing

:eek:

You'll get no naked pictures of me!

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

iMook

Jun 3, 2003, 11:06 AM

:D scem0: no s---, Sherlock.

vniow

Jun 3, 2003, 12:28 PM

Originally posted by springscansing

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

Eeerrr....not quite..

GeneR

Jun 3, 2003, 04:08 PM

Originally posted by springscansing

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?

Dang. Binomials. My arch enemy...

It's been about 15 years but here's a go (I know people have probably solved it but I've got to start using my brain at some time.... :D)

If n > 0

4x^2 + kx + 25 = (2x + n)^2 for all x, what is the value of k+n....

4x^2 + kx + 25 = 4x^2 + 4xn + n^2 for all x.

Cross out 4x^2 on both sides...

kx + 25 = 4nx + n^2

kx + 5^2 = 4nx + n^2

Hmmm. Okay, now if it's for "all x"...then that means k has to be positive because n is positive.

So, that means that n+k will be a positive value.

n>0, k>0, if x can be either + or -.

Hmmm. My head hurts... I think I gotta go lie down now. :D

shadowfax

Jun 3, 2003, 04:11 PM

dude, we already figured out the entire thing last night at 3:00 AM central time. and you didn't even finish solving it :p

GeneR

Jun 3, 2003, 04:15 PM

Originally posted by Shadowfax

dude, we already figured out the entire thing last night at 3:00 AM central time. and you didn't even finish solving it :p

Shhhh. I'm recuperating. I'm not used to thinking... :D

MacBandit

Jun 3, 2003, 04:47 PM

Originally posted by GeneR

Shhhh. I'm recuperating. I'm not used to thinking... :D

Do I smell smoke? Yup I'm sure I smell smoke. Maybe you should relax some I think your heads on fire.:p :D

GeneR

Jun 3, 2003, 04:55 PM

Originally posted by MacBandit

Do I smell smoke? Yup I'm sure I smell smoke. Maybe you should relax some I think your heads on fire.:p :D

Yeah, feeling a bit like Michael Jackson at the moment... can't... concentrate... must... breath...deeply...can't...think...and...chew... gum... at... the... same... time... :D

zarathustra

Jun 3, 2003, 05:17 PM

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

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

kx+25=4nx+n^2

4nx+n^2+kx=25 -> k=(25-4nx-n^2)/x

4nx+n^2+x((25-4nx-n^2)/x)=25

4nx+n^2+(25x-4nx^2-xn^2)/x^2=25 -> x=0

n^2=25

n=5

shadowfax

Jun 3, 2003, 05:23 PM

Originally posted by zarathustra

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

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

kx+25=4nx+n^2

4nx+n^2+kx=25 -> k=(25-4nx-n^2)/x

4nx+n^2+x((25-4nx-n^2)/x)=25

4nx+n^2+(25x-4nx^2-xn^2)/x^2=25 -> x=0

n^2=25

n=5 wtf? how many times do we need to have this problem solved?

zarathustra

Jun 3, 2003, 05:51 PM

Originally posted by Shadowfax

wtf? how many times do we need to have this problem solved?

Please ignore. I did not bother reading all the posts, just wanted to see if I could do it... Keep your panties on, no reason to get all excited. :p

shadowfax

Jun 3, 2003, 05:56 PM

Originally posted by zarathustra

Please ignore. I did not bother reading all the posts, just wanted to see if I could do it... Keep your panties on, no reason to get all excited. :p it's a little hot down here to be keeping my panties on. plus, you know, they are so obtrusive when you get excited and you just want to... mmmm... you would know about that, i am sure, seeing how you get off on math without even paying attention.

this problem has been solved three times already. it's almost insulting to spring's intelligence. you have a responsibility as a poster to make sure what you say hasn't already been said on a post. and when you slip up, there's no call to treat me like a jerk because i commented on your redundancy.

King Cobra

Jun 3, 2003, 06:42 PM

Are we talking about improving SAT scores, or are we discussing user pics?

I'm not saying that's a bad thing, of course. :D

But to quickly keep this on topic, I could never get my SAT scores (or PSAT for that matter) above 1000. My English scores on both the PSAT and SAT were 300. I found it so hard to analyze and interpret words and stories.

The math, of couse, was easy, but I must have made some uncaught errors within the test.

This particular Math problem has been beaten to death, just like the poor horse. I have a particular Math problem I have never been able to solve, even after over 6 hours of non-consecutive work.

But it's well above the SAT level.

Rower_CPU

Jun 3, 2003, 06:44 PM

Anyone wanna have a go w/ GRE scores? :p

Let's keep it civil in here folks...

janey

Jun 3, 2003, 06:49 PM

Originally posted by iMook

4. Drink coffee/caffeinated-something (I prefer Frappuccino) and eat something sweet before taking the test, but not right before. Energy boost.

heh not for me.

drank like two cups of some starbucks thing (don't quite remember what it was), then a frappuccino, and went to take the SAT.

i fell asleep. eh. i did bad though i got like ~1300. that was two years ago (do the math...yes i was in 6/7th grade). hopefully when i do other tests and stuff, i won't fall asleep :p :eek:

King Cobra

Jun 3, 2003, 07:01 PM

I don't think it was the coffee that made you fal asleep. I don't even feel coffee is supposed to help your score better on tests or quizzes.

Coffee just makes you hyperactive and sweaty, if it's real hot. :eek: :eek:

scem0

Jun 3, 2003, 07:06 PM

and then real tired a while after you drink it.... :rolleyes:

cubist

Jun 3, 2003, 07:34 PM

Say, springscansing, how do you parse your name?

spring scan sing

or

springs can sing

or some other way?

Doctor Q

Jun 3, 2003, 08:01 PM

You guys have stopped talking about the math problem, but something occurred to me. Was this a multiple choice problem? Remember that one way to solve an SAT problem is to try each of the possible answers (picking sample values for any other unknowns). It may seem like cheating but it isn't, and it can save you lots of time when you don't actually have to solve the equations.

Rower_CPU

Jun 3, 2003, 08:58 PM

Originally posted by Doctor Q

You guys have stopped talking about the math problem, but something occurred to me. Was this a multiple choice problem? Remember that one way to solve an SAT problem is to try each of the possible answers (picking sample values for any other unknowns). It may seem like cheating but it isn't, and it can save you lots of time when you don't actually have to solve the equations.

Yup. Plug the middle answer in and see how it fits. If it's too big go smaller, and vice versa. You can cut it down pretty quick w/out trying all the options.

springscansing

Jun 3, 2003, 09:01 PM

No it was a grid-in.

springscansing

Jun 3, 2003, 09:02 PM

Originally posted by scem0

no, the girl in the picture is attractive. :rolleyes: ;)

For the love of god scem0 stay off my threads. If there's one person I can't stand here, its you. One more pointless comment and I'll scream.

MacBandit

Jun 3, 2003, 09:10 PM

Originally posted by Shadowfax

it's a little hot down here to be keeping my panties on. plus, you know, they are so obtrusive when you get excited and you just want to... mmmm... you would know about that, i am sure, seeing how you get off on math without even paying attention.

this problem has been solved three times already. it's almost insulting to spring's intelligence. you have a responsibility as a poster to make sure what you say hasn't already been said on a post. and when you slip up, there's no call to treat me like a jerk because i commented on your redundancy.

Calm down. I personally find it interesting to see it worked out in so many different ways. For those of us that have been out of the math thing for a few years it's good to see it all step by step by step which you two kind of skipped a few right in the beggining.

Thanks for caring though.:p

springscansing

Jun 3, 2003, 09:13 PM

Originally posted by MacBandit

Calm down. I personally find it interesting to see it worked out in so many different ways. For those of us that have been out of the math thing for a few years it's good to see it all step by step by step which you two kind of skipped a few right in the beggining.

Thanks for caring though.:p

No Shadow was right. It's getting bloody annoying.

As for my name cubist: Springs Can Sing

It's from a Nurse With Wound song if you're familiar with them....

shadowfax

Jun 3, 2003, 10:16 PM

Originally posted by MacBandit

Calm down. I personally find it interesting to see it worked out in so many different ways. For those of us that have been out of the math thing for a few years it's good to see it all step by step by step which you two kind of skipped a few right in the beggining.

Thanks for caring though.:p i see your point, and somewhat agree, though i could kind of tell last night that springs was getting a little edgy about it (and i was right), but what annoyed me was that he effeminated me for his own laziness and stupidity. that's pathetic.

springscansing

Jun 3, 2003, 10:19 PM

Wait.. what did I do? lol

shadowfax

Jun 3, 2003, 10:26 PM

you killed a bunch of cats because we told you we all thought you were stup--

i mean, you sounded like you were maybe getting annoyed last night that we kept saying the same thing multiple times.

springscansing

Jun 3, 2003, 10:30 PM

hehe, nah I wasn't. I'm not even annoyed today. I just don't like macbandit. *dance*

shadowfax

Jun 3, 2003, 10:36 PM

Originally posted by springscansing

hehe, nah I wasn't. I'm not even annoyed today. I just don't like macbandit. *dance* oh, well, there's all-consuming hatred of random MR users to boot then. alright!

sparkleytone

Jun 3, 2003, 10:43 PM

*dance*

*dance*

ooooh.

Rower_CPU

Jun 3, 2003, 11:14 PM

Since this has turned into a spamfest...