Question

find a quadratic polynomial whose zeros are reciprocal of the zeros of the polynomial f(x) = ax²+bx+c where a and c unequal 0​

Answer 1

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Let p,q be zeros of ax2+bx+c

∴p+q=a−b  &  pq=ac

Let P & Q be zeros of required polynomial

It is given that P= 1/p , Q=1/q

Then,

P+Q=p1+q1=pqq+p=c/a−b/a=c−b

PQ=p1.q1=pq1=ca

∴ Required polynomial = x2+cbx+ca⇒cx2+bx+a

Answer 2

Refer this attachment

Hope it's helpful for you.