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factor of t..then k=

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factor of t..then k=

by mknmknmkn » Fri Sep 17, 2010 5:44 am
Problem 55 in GMAT Quantitative Review, I still don't understand after looking at the explanation.

If (T-8) is a factor of T^2-KT-48, then K=

(A) 16
(B) 12
(C) 2
(D) 6
(E) 14

The correct answer is C. According to the book, but I don't understand. Can someone shed some light on this for me?
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by kvcpk » Fri Sep 17, 2010 6:43 am
If (T-8) is a factor of T^2-KT-48, then K=?

If T-8 is a factor, it means that 8 is a root of the eqtn.

Remember this.
in the eqtn: ax^2+bx+c, sum of the roots = -b/a and product of roots = c/a

now,
in the eqtn, T^2-KT-48, a=1, b =-k, c= -48

We know that one root is 8. Let the other root be P
P+8 = -b/a = k
P(8) = c/a = -48
P=-6

Substitute in the above:
-6+8 = k

Hence k=2.

Hope this helps!!
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by debmalya_dutta » Fri Sep 17, 2010 7:26 am
mknmknmkn wrote:Problem 55 in GMAT Quantitative Review, I still don't understand after looking at the explanation.

If (T-8) is a factor of T^2-KT-48, then K=

(A) 16
(B) 12
(C) 2
(D) 6
(E) 14

The correct answer is C. According to the book, but I don't understand. Can someone shed some light on this for me?
Since T-8 is a factor , it means that when T=8 , then the equation T^2-KT-48 = 0
So, substitute value of T as 8 in the equation
K = 2

What Praveen has identified in his note is something good to know .
@Deb
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by mknmknmkn » Sat Sep 18, 2010 7:54 am
It was so obvious but I didn't get it. Now I got it, thanks!

Level up!
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