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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]  24 Jan 2014, 02:53
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Question Stats:

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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

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600

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Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4225

Kudos [?]: 40978 [1] , given: 5654

Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  24 Jan 2014, 02:53
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KUDOS
Expert's post
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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: $$8^2 - 8k - 48 = 0$$ --> $$k = 2$$.

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  24 Jan 2014, 04:55
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.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  24 Jan 2014, 22:27
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KUDOS
Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.
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If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  24 Jan 2014, 23:46
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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, $$k = 8 + (- 6) = 2$$

Last edited by arunspanda on 01 Nov 2014, 02:02, edited 1 time in total.
Math Expert
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Posts: 27215
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Kudos [?]: 40978 [0], given: 5654

Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  25 Jan 2014, 11:39
Expert's post
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: $$8^2 - 8k - 48 = 0$$ --> $$k = 2$$.

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  25 Feb 2014, 18:44
-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
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GMAT 1: 750 Q48 V46
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Kudos [?]: 172 [0], given: 116

Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink]  22 May 2014, 23:38
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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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=   [#permalink] 22 May 2014, 23:38
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