SOLUTION

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

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

\((t - 8)\) is a factor of \(t^2 - kt - 48\) means that \(t = 8\) is a solution of the equation \(t^2 - kt - 48 = 0\).

Substitute\(t = 8\) to get the value of k: \(8^2 - 8k - 48 = 0\) --> \(k = 2\).

Answer: C.
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Factoring the expression:
(t - 8) (t - ?), since (t - 8) is a factor, the other bracket has to be (t + 6).
The net result is -2. So (B)? Not sure of the answer because I got lost with the signs a bit.

Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.

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

(A) - 6
(8) - 2
(C) 2
(0) 6
(E) 14

It is given that \((t - 8)\) is a factor of the quadratic expression \(t^2 - kt - 48\)
Hence, we need to find the other factor of \(-48\) such that the sum of factors is\(-(\frac{-k}{1})=k\).

Thus, \((8) * x = -48\)

Or, \(x = -6\)

So, \(k = 8 + (- 6) = 2\)

Answer: (C)

-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
k=2 Answer = C

Vieta's formulas applied to quadratic: x1+x2= -b/a & x1*x2=c/a
From what is given in the question: -8+x2=-k and -8*x2=-48
so, x2=6 and thus -8+6=-k i.e. k=2
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since (t-8) is a factor, then: (8)^2 - 8k - 48 = 0,
-8k = -16
k = 2.
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In this question, I didn't understand this step:

(t−8)(t−8) is a factor of t2−kt−48t2−kt−48 means that t=8t=8 is a solution of the equation t2−kt−48=0t2−kt−48=0.

Why do we assume both equations are equal to 0?
What is the rationale of this step? It would be great if someone could explain with examples, or with videos.

---->Your red part is somewhat mistake; you can't find (t-8)(t+6) = t^2 - 14 -48. Actually, (t-8)(t+6)=t^2-2t-48.
***Can someone explain how the answer isnt 6?
---->if you put put the value of k=6 in t^2 - kt - 48, then you can't find (t-8) as a factor. So, that's why it wrong. But, if k=2, then
t^2 - kt - 48=t^2 - 2t - 48=>t^-8t+6t-48=>t(t-8)+6(t-8)=>(t-8) (t+6). So, the green part is the factor according to question stem.
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We were asked to find the value of k but not the factors of the given expression. -6 will be a factor of the expression, apart from 8. If you want to know k, substitute 8 in the value of t or -6, both will give you the value of K as 2. Here by using 8 directly, gives us the result quicker.

Hope this helps

Since (t - 8) is a factor of t^2 - kt - 48, t = 8 must be a root of the equation t^2 - kt - 48 = 0. We can substitute 8 for t and determine a value for k.

8^2 - 8k - 48 = 0

64 - 8k = 48

-8k = -16

k = 2

Answer: C
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This problem is a good one in a few ways because it has a trap that's useful to learn from and it can be solved in two ways.

The simplest method is to realize that t = 8 is a root of the quadratic (as given), plug it into the equation and solve for k directly.

8^2 - k(8) - 48 = 0
K =2

The other method involves breaking up the quadratic into its roots: (t-8)(t+6) = 0
-Kt = -8t + 6t by FOIL
-k = -2
k = 2

However, it's common to set kt = -2t and thus set oneself up for the trap k = 2, one of the answer choices. So it's important to remember that -kt is an entire term, not just kt itself, so you need to set the entire term = -2t.

hello Bunuel
hope my solution finds you well!

I would appreciate if you could let me know if my solution is correct!


t-8 = k
t = k+8
Plug in T into t^2 - kt – 48
- k^2+8^2 – k(k+8) – 48
-k^2+8^2 – K^2-8k– 48
After i eliminate k^2; and – K^2
I get this 64-8k-48
-8k= -64+48
-8k= -16
then k = 2

Ans K = 2

[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

STEP 1 prime factorise 48 and find the other root . SO T= 8 and other root will be t=-6 .

step 2 now we know sum of roots will be -8 +6 = -2 this value is equal to - K (not just k).
hence -K = -2 => K = 2 .

Hi,

The answer assumes that the quadratic equation equals to zero. Does this mean all quadratic equation will equal zero even though it is not stated explicitly?

Yeah that is my question too. Why do we assume all quadratic equation will equal to zero unless it is stated? I failed to solve this problem due to this issue. I did not assume the quadratic will equal to zero.

Did anyone reply to your question or do you know the answer already?

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