Question

If α and β are zeroes of the polynomial f(x)=x2+px+q then find the quadratic polynomial having 1/α and 1/β as its zeroes

Answer 1

Given  α and β are zeroes of the polynomial f(x)=x2+px+q

α+ β = -p αβ = q

(1/α + 1/β) = (α + β) / αβ  = - p / q

1/αβ  = 1 / q.

If 1/α, 1/β are zeros of the quadratic polynomial then the equation is

 x2 -(1 / α + 1 / β)x + 1 / αβ = 0 then

x2 -(-p / q)x + 1 / q = 0

qx2 + px + 1  = 0