Problem Solving

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

-6
-2
2
6
14

The OA is C. However I got B. Although I understand the Official Guide's way of solving it, I solved it in the following manner and got a different answer:
t^2-kt-48 then it follows that
(t-8)(t+6) =0 (Because -8*6=-48) Therefore;
k must be the sum of -8 and 6, which is -2 option B. Can anyone tell me where I went wrong? Thanks

The Official Guide solves it by plugging 8 in for t and solving the equation. Again, I understand why/how this works, but I don't understand why/how my approach is wrong.

Thanks

Alex,

Your approach is right except what you forgot was that you needed to find the value of k, not the sum of the roots.

You found the sum of the roots to be -2. But the equation is in t^2-kt-48 form. Therefore, -k = -2, making k =2.

Regards
Anup