Question

If and are the zeroes of the polynomial f(x)=

2 + px + q, then what is the polynomial

having 1/ and 1/ as its zeroes?​

Answer 1

Answer:

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