The equation $x^3 + 8x^2 - 4x + c = 0$ has three roots, one of which is the sum of the other two. What is $c$?

Call the roots   a , b , a + b

By Vieta

a + b + a + b  =  -8   

So

2 (a + b) =  -8

a + b =  -4

And

ab + a (a + b)  +  b(a + b)   = -4

ab + a (-4) + b (-4)  = -4

ab  - 4(a + b) =  -4

ab - 4(-4)  =  -4

ab + 16  =  -4

ab =  -20

And finally

a * b * ( a + b)  =  -c

ab * ( a + b)  = -c

-20 * -4 = -c

80  =  -c

-80 = c

P.S ....  the roots are  -2 ± 2sqrt (6)  and  -4