Question

if alpha and bheta zeros of polynomial f(x)=axsquare +bx+c<br />1. 1 upon a alpha +b +1 upon a bheta +b <br />2. bheta upon a alpha +b + alpha a bheta +b

Answer 1

We already know that 

α + β = -b/a

=> a(α + β) = -b

=> -a(α + β) = b


Substituting this value of b in the problem,


=> 1/(aα + b) + 1/(aβ + b)

=> 1/(aα - a(α + β)) + 1/(aβ - a(α + β))

=> 1/(-aβ) + 1/(-aα)

=> -1/a (1/β + 1/α)

=> -1/a (α + β)/αβ

=> -1/a (-b/a)(c/a)

=> b/ac