Question

Find the quadratic polynomial whose zeroes are reciprocal of the zeroes of polynomial f(x) = ax^2 +bx+c,a not = 0,c not=0

Answer 1

Answer:

cx² + bx + a

Step-by-step explanation:

f(x) = ax² + bx + c = x²( c(1/x)² + b(1/x) + a ) = x² g(1/x),

where g(x) = cx² + bx + a.

So f(x) = 0 <=> g(1/x) = 0.

That is, the zeros of g(x) are the reciprocals of the zeros of f(x), as required.