how to find the value of alpha and beta here is a question :

if $a$ and $b$ are the zero of polynomial $ f(x)=2x^2-9x+9$, then $1/a+1/b$ is equal to :
(a) $9/2$     (b)  $3/9$      (c)  $1$   (d) $-1$

which is the correct answer?
well actually $a $ and $b$ are alpha and beta here.
i solve upto here :
$a+b = 9/2$, and $ab = 9/2$
because alpha + beta = -b/a and alpha*beta = c/a. i tried to reciprocal a+b but that will come to 2/9 but here  the answer is 1 !  
and after that i got confused.....(answer is: c)

You know that $ab=\frac92$ and $a+b=-\frac{-9}{2}=\frac92$. In fact given a 2-degree polynomial $Ax^2+Bx+C$, the sum of the roots is $-\frac{B}{A}$, while their product is $\frac{C}{A}$.
So$$\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}=\frac{\frac92}{\frac92}=1$$
