factor of t..then k=

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

mknmknmkn: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jun 23, 2010 1:44 pm

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?

Quote

Source: Beat The GMAT — Problem Solving | Fri Sep 17, 2010 5:44 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pm; Thanked: 215 times; Followed by:7 members

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!!

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

Quote

debmalya_dutta: Master | Next Rank: 500 Posts; Posts: 385; Joined: Sun Jul 12, 2009 10:16 pm; Thanked: 29 times; Followed by:2 members; GMAT Score:710

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