Question

find a quadratic polynomial whose zeros are reciprocals of the zeros of the polynomial p(x)=ax^2+bx+c,a and b not zeros
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Answer 1

Answer:

Let zero es of ax^2+bx+c be p and q

p+q=-b/a

pq = c/a

(p+q)/(pq)= -b/c

1/q + 1/p = -b/c = sum of two roots of new polynomial

product of two roots of new polynomial = 1/pq) = a/c

So the new polynomial is:

x^2-(-b/c)x +(a/c)

cx^2 + bx + a