= (x-1)*(x-2),

so 1 and 2 are the roots of the given polynomial of the degree 4.


The fact that x= 1 is the root of the given polynomial of the degree 4 means

1^4 +k*1^3 -10*1^2 - 20*1 + 24 = 0,   or

1 + k - 10 - 20 + 24 = 0,   which implies  k = 5.


According to Vieta's theorem, the sum of the roots of the given polynomial of the degree 4 is equal 

to the coefficient at x^3 taken with the opposite sign, i.e. -5.