Question 1105536
x^2-3x+2 factors into (x-2)(x-1), so x=1 and 2 are roots.
x^4+kx^3-10x^2-20x+24=0
16+8k-40-40+24=0
8k-40=0
k=5
the polynomial is x^4+5x^3-10x^2-20x+24
synthetic division with 2

2/1===5===-10===-20===24
==1==7=====4=====-12===0
x^3+7x^2+4x-12
-2/1===7===4===-12
==1===5===-6===0
x^2+5x-6, so -2 is a root
(x+6)(x-1)=0, and 1 is already known to be a root, so -6 is the other root.
The sum of -6, -2, 1, 2 is -5. ANSWER.
{{{graph(300,300,-10,10,-1000,1000,x^4+5x^3-10x^2-20x+24)}}}