If $f(x)$ is a polynomial of degree three leaves remainder $1$ when divided by $(x−1)^2$ and leaves remainder $–1$ when divided by $(x+1)^2$ 
$f(x)$ is a polynomial of degree three which leaves remainder $1$ when divided by $(x−1)^2$ and leaves remainder $–1$ when divided by $(x+1)^2$.
If $f(x)=0$ has roots $\alpha,\beta,\gamma$, then $$(\alpha\beta+\beta\gamma+\gamma\alpha)=\text?$$

The answer to the question is $-3$. How do I approach this problem?

Hint
Let $f(x)=1+(x-1)^2(ax+b)=-1+(x+1)^2(cx+d)$
$ax^3+x^2(b-2a)+x(a-2b)+b-1=cx^3+x^2(d+2c)+x(c+2d)+d+1$
Now compare the coefficients of the different exponent of $x$
$\implies c=a$
$b-1=d+1\iff d=b-2$
$b-2a=d+2c\iff b=d+2(c+a)=d+4a$
$a-2b=c+2d\implies b=-d=2-b$
Hope you can take it from here?
