A question on roots of a Quadratic.

Question

If roots of the equation ${ax}^2+bx+c=0$ are of the form $$\frac{\alpha}{\alpha-1},\frac{\alpha+1}{\alpha}$$ Then the value of $$({a+b+c})^2$$ I have no clue how to approach this one, any help is appreciated!

Answer 1

From the form:

$\frac{1}{x} + x = 2$ => $x^2 + x -2 = 0$, and first equation is $kx^2 + kx - 2k = 0$. So, $(a+b+c)^2=0$