[tex](X-1)^3 \,\,|\,\, f \Rightarrow f(1) = 0,\quad f'(1) = 0,\quad f''(1) = 0[/tex]
[tex]f = ax^4+bx^3+cx^2+(a-1)x-1\\ \\ f(1) = a+b+c+(a-1)-1 = 0\\f'(1) = 4a+3b+2c+(a-1)= 0 \\ f''(1) =12a+6b+2c = 0 \\ \\ 2a+b+c = 2 \\ 5a+3b+2c = 1 \\ 6a+3b+c = 0 \\ \\ 6a+3b+c = 0 \\ 6a+3b+3 c = 6 \\ \\ 2c = 6 \Rightarrow c = 3 \\ \\ a-c = -1 \Rightarrow a = 2\\ \\ 4+b+3=2 \Rightarrow b = -5\\ \\ \\ \Rightarrow S =a+b+c = 2+3-5 = 0[/tex]
