Problem Solving

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..?

(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

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