is alpha and beta are zeros of the polynomial f(x)=x²+px+q then polynomial having 1/alpha and 1/beta as its zeros is:

(A)x²+qx+p

(B)x²-px+q

(C)qx²+px+1

(D)px²+qx+1

The answer I think is qx²+px+1.

Alpha+Beta = -b/a

b = p & a = 1

So, Alpha+Beta = -p

And, Alpha x Beta = c/a

c = q & a = 1

So, Alpha x Beta = q

Now, The polynomial having 1/alpha & 1/beta as its zeroes will have-

1/alpha+1/beta = -b/a [Sum of the zeroes of the new polynomial]

Taking alpha x beta as LCM:-

beta+alpha/alpha x beta = -b/a

We know, that alpha+beta = -p & alpha x beta = q. Put them in this equation:-

-p/q = -b/a ------(i)

Now, 1/alpha x 1/beta = c/a [Product of the zeroes of the new polynomial]

1/apha x beta = c/a

we know, that alpha x beta = q. Put it in this equation:-

1/q = c/a ---------(ii) 

On comparing (i) & (ii) you will find that  b = p, a = q & c = 1 of the new polynomial.

The general form is ax²+bx+c

Hence the new polynomial is qx²+px+1.

However I am not quite sure if this is correct or not. So, a meritnation expert should answer this.