factor

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Ramit88: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Fri Nov 26, 2010 8:25 am; Thanked: 3 times

by Ramit88 » Tue Jan 25, 2011 10:00 pm

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

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

ANS C

my ans is coming C
my method
-48 = -6 X -8

whats the mistake m making..?

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Source: Beat The GMAT — Problem Solving | Tue Jan 25, 2011 10:00 pm

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Tue Jan 25, 2011 10:05 pm

(t-8) is a factor of t^2 - kt - 48 then
(t-8)(t-p) = t^2 - kt - 48 assuming p as another factor
also (t-8)(t-p) = t^2 - (p+8)t + 8p = t^2 - kt - 48
=> 8p = -48 or p=-6

=>2t=kt or k=2

Charged up again to beat the beast

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eyelikecheese: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Sun Nov 14, 2010 8:46 am; GMAT Score:690

by eyelikecheese » Tue Jan 25, 2011 10:07 pm

For quadratic equations, there are two values. The root and the factor. In this case, the factor is (t-8) and thus the root is 8 because 8-8=0

So your looking for the value that multiplies by +8 to give you -48. This number is -6. Therefore, the factor is (t-6) and the root is +6. The value for K is therefore 8-6=2

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