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If (t-8) is a factor of t^2-kt-48, then k=

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If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 08:41
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If (t-8) is a factor of t^2-kt-48, then k=

A. 16
B. 12
C. 2
D. 6
E. 14

[Reveal] Spoiler:
OA is C

OE is:
If (t-8) is a factor of the expression t^2-kt-48, then the expression can be written as the product (t-8)(t+a). Where did the a come from? How do figure out to use a (or any other unkown)?
t^2-8t+at-8a multiply the binomials
t^2-(8-a)t-8a combine the t terms

Comparing this expression to the original expression sets -8a=-48 or a=6. Then, by substituting this value of a into the product of (t-8)(t+a):

(t-8)(t+6)
t^2-8t+6t-48
t^2-2t-48
Therefore, k=2

Thanks for any help!


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-t-8-is-a-factor-of-t-2-kt-48-then-k-166573.html
[Reveal] Spoiler: OA
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 14:29
If (t-8) is a factor of t^2-kt-48, then k=

A. 16
B. 12
C. 2
D. 6
E. 14

t^2-kt-48 = (t-8)(t+m) where m is any positive integer.

if 48/8 = 6, then we know as a matter of fact that:
m = +6
and thus k = 8-6 = 2


This is very basic algebra: for m and a are positive integers
t^2-kt-m = (t-a)(t+m) where a>m
t^2+kt-m = (t-a)(t+m) where a<m
t^2-kt+m = (t-a)(t-m)
t^2+kt+m = (t+a)(t+m)

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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 15:21
First, recognize t^2-kt-48 as a quadratic equation. That is, it is the product of 2 binomials (2 term polynomials) The first factor is given: (t-8). We know that the second factor will be (t+something) - the explanation uses "a" for the unknown. The rule for multiplying 2 binomials together is summarized by the acronym FOIL (first, outer, inner, last) So with the 2 terms (t-8) (t+a), the product would be t^2+at-8t-8a. If you look at the original equation, you see that the last term is -48, which correlates to -8a. So a=-48/-8 = 6. Plug 6 back into the place of a for "t^2+6t-8t-48". Simplify: t^2-2t-48. So k=2.
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 15:41
It should be noted that any equation of the second degree can be broken down to the form that the OE used.

Remember the formula [-b +/- sqrt(b^2 - 4ac)]/2a to find the two possible roots for an equation of the form ax^2+bx+c = 0.

Hope this helps.

Last edited by ioiio on 23 Jul 2007, 16:11, edited 1 time in total.
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 16:04
ishcabibble wrote:
Basically, I'm looking for a clearer explanation on this one:

If (t-8) is a factor of t^2-kt-48, then k=

A. 16
B. 12
C. 2
D. 6
E. 14

OA is C

OE is:
If (t-8) is a factor of the expression t^2-kt-48, then the expression can be written as the product (t-8)(t+a). Where did the a come from? How do figure out to use a (or any other unkown)?
t^2-8t+at-8a multiply the binomials
t^2-(8-a)t-8a combine the t terms

Comparing this expression to the original expression sets -8a=-48 or a=6. Then, by substituting this value of a into the product of (t-8)(t+a):

(t-8)(t+6)
t^2-8t+6t-48
t^2-2t-48
Therefore, k=2

Thanks for any help!


iscabible,

don't worry about mishari's condescending banter... nerds get very upset when people in the real world can't solve math problems and don't obsess over the properties of numbers and other mathmetical nonsense that is of little use to 95% of tomorrow's managers and leaders. Also, recognize that many people on these boards come from parts of the world where where rote learning is the dominant system of education (i.e. memorization for little else besides recitation vs. true comprehension, creativity etc...)

anyway, like the others have mentioned recognize that this is a quadratic. while you need to memorize the quadratic forumla, it is not necessary in this problem; memorizing the basic forms of a quadratic that mishari listed can be a real time saver - but it is more important to be able to derive them and understand them first rather than learn them rote.

the OG explanations at times see counterintuitive. They are not Kaplan etc... they DO NOT CARE if you do well on the test. keep this in mind when reading their explanations. they are not going to necessarily show you the best way to solve a problem

in this problem they are giving you one of the roots as (t-8) you need to find t + or - something... when you use the foil method the product of the last two terms must equal -48. -8*6=-48. so we have that the other root is t+6. now with FOIL the sum of the products of the inner and outer terms = the middle term of the quadratic. 6t-8t=-2t. a value of 2 for k gives you -2t
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 16:09
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If t-8 is a factor of the equation, then when t = 8, the equation must become zero.

So

64-8k-48 = 0
k = 2
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 16:14
ywilfred wrote:
If t-8 is a factor of the equation, then when t = 8, the equation must become zero.

So

64-8k-48 = 0
k = 2

Good point! That's what I love about this board - seeing the different ways people tackle a problem to come up with the same answer. Learning to use these methods will put alot of tools in our toolboxes when we go in to take the test.
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 23 Jul 2007, 16:15
ywilfred wrote:
If t-8 is a factor of the equation, then when t = 8, the equation must become zero.

So

64-8k-48 = 0
k = 2


Why didnt I think of this? Definitely easier than finding roots and imagining quadratic equations.

Sometimes we all over-complicate things thanks to the ever-increasing number of formulae we tend to remember.
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 24 Jul 2007, 05:18
Thanks everyone for your help! I did see that it is a quadratic equation, but for some reason adding that extra unknown just totally threw me off. Unfortunately for me, my brain just has a really hard time thinking that way. At least I rock on the verbal section!

Robin in NC, thanks for your very clear explanation - that's exactly what I was looking for. And ywilfred, that is a genius way of thinking about it! I'm sure that you're going to save a lot of us a lot of time on the test now! And thanks for the words of encouragement, anonymousegmat! Trust me, it is probably way more frustrating for me not being able to wrap my mind around certain concepts than it is for anyone else. :-D
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 24 Jul 2007, 06:29
ishcabibble wrote:
Basically, I'm looking for a clearer explanation on this one:

If (t-8) is a factor of t^2-kt-48, then k=

A. 16
B. 12
C. 2
D. 6
E. 14

OA is C

OE is:
If (t-8) is a factor of the expression t^2-kt-48, then the expression can be written as the product (t-8)(t+a). Where did the a come from? How do figure out to use a (or any other unkown)?
t^2-8t+at-8a multiply the binomials
t^2-(8-a)t-8a combine the t terms

Comparing this expression to the original expression sets -8a=-48 or a=6. Then, by substituting this value of a into the product of (t-8)(t+a):

(t-8)(t+6)
t^2-8t+6t-48
t^2-2t-48
Therefore, k=2

Thanks for any help!



Hi

t-8 is one of the factors of this quadratic equation. Hence t =8.

Subsititute t=8 in the equation and you get 64-8k-48.

Eqaute it and you get k = 2.

Regards

Nikhil
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 26 Jul 2010, 10:55
Almost every time I get stumped on a problem, I come here to post it and then figure out what I did wrong as I post or right after!

If \((t-8)\) is one factor, then the second factor would have to be \((t+6)\) to satisfy the -48 part.

A. is a trap answer, because -6 is the root, but that is not what the question is asking for!

\(-8 + 6 = -2\)

B. is another trap answer, because the negative sign is already given in the original equation.

Therefore, the correct answer is \(k = 2\).
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 27 Jul 2010, 03:30
Hi,

For quadratic equations in the form ax^2+bx+c=0, you can make use of the following:
Sum of the roots: x1+x2 = - b/a
Product of the roots: x1*x2 = c/a


regards,
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 27 Jul 2010, 05:19
jpr200012 wrote:
If \((t-8)\) is a factor of \(t^2-kt-48\), then \(k =\)

A. -6
B. -2
C. 2
D. 6
E. 14


If \((t-8)\) is a factor of \(t^2-kt-48\)

then \(t =8\) must satisfy \(t^2-kt-48=0\)

=> \(8^2 -8k - 48 = 0\) => \(8 -k -6 = 0\) => \(k =2\)
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 12 Oct 2010, 05:00
I have to say that it is pretty cool and kind of funny that I'm still getting responses from a post I wrote 3 years ago. Especially since I'm now done with my MBA!

I'm glad that this thread is still helping folks and good luck on the GMAT!
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 15 Nov 2010, 19:49
I am having problem with this question.

The quadratic equations has the form ax^2+bx+c=0

The question stem has: t^2-kt-48. One root of the equation is 8 (as given), which means the other one is 6.
So then the equation start looking like this: t^2-2t-48.

Going back to a generic formula for quadratic equation: a=1, b=-2, c=-48.
So the question asks what is "k", meaning that they ask for the absolute value of "b"?
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 15 Nov 2010, 20:04
Expert's post
Fijisurf wrote:
I am having problem with this question.

The quadratic equations has the form ax^2+bx+c=0

The question stem has: t^2-kt-48. One root of the equation is 8 (as given), which means the other one is 6.
So then the equation start looking like this: t^2-2t-48.

Going back to a generic formula for quadratic equation: a=1, b=-2, c=-48.
So the question asks what is "k", meaning that they ask for the absolute value of "b"?


To answer your question:
General form: ax^2+bx+c=0
Here the equation is t^2-kt-48 = 0
So -k = b or we can say k = -b
When you get the equation t^2-2t-48 = 0, you get b = -2. So k = - (-2) = 2

Something to note: Given t^2-kt-48 = 0
You got the equation is t^2-2t-48 = 0
Just compare the two right here and you see that k = 2

Another approach: When we say 8 is a root of the equation, we mean it satisfies the equation.
So if I put 8 in place of t, it should satisfy my equation.
t^2-kt-48 = 0 will become 8^2 -8k - 48 = 0 or k = 2
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 15 Nov 2010, 21:28
VeritasPrepKarishma wrote:
Another approach: When we say 8 is a root of the equation, we mean it satisfies the equation.
So if I put 8 in place of t, it should satisfy my equation.
t^2-kt-48 = 0 will become 8^2 -8k - 48 = 0 or k = 2


Thanks, it makes sense.
On a separate note:
The question stem said that (k-8) is factor of t^2-kt-48.
But it does not mean that t^2-kt-48 equals to zero? (as you wrote above), right?
Or I am missing something?
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 16 Nov 2010, 04:49
Expert's post
Fijisurf wrote:
On a separate note:
The question stem said that (k-8) is factor of t^2-kt-48.
But it does not mean that t^2-kt-48 equals to zero? (as you wrote above), right?
Or I am missing something?


You are right. Expression t^2-kt-48 does not imply that it is an equation. But we have that (t-8) is a factor of t^2-kt-48. When I say (t - 8) is a factor of t^2-kt-48, it means that I can write t^2-kt-48 as (t - 8)*(t - a) where a is some constant. Now, 8 and a (which we know to be -6) will be the roots of the equation t^2-kt-48 = 0. i.e. if I put t = 8, the expression will become 0.
Therefore, to use the fact that if t = 8, this expression will become 0, I wrote it in equation form to get the value of k.
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 16 Nov 2010, 10:35
I think is the best way and fastest to solve this problem

Another approach: When we say 8 is a root of the equation, we mean it satisfies the equation.
So if I put 8 in place of t, it should satisfy my equation.
t^2-kt-48 = 0 will become 8^2 -8k - 48 = 0 or k = 2
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Re: If (t-8) is a factor of t^2-kt-48, then k= [#permalink] New post 16 Nov 2010, 10:48
Thanks guys.
This question is from very beginning of Official GMAT Math review. So, I suppose it is on the easier side.
However, it has some kind of twist I just could not get.
Re: If (t-8) is a factor of t^2-kt-48, then k=   [#permalink] 16 Nov 2010, 10:48

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