Let α,β be the roots of x2+bx+1=0 . Then the equation  whose roots are −α+1β and −β+1α is

Since α,β are roots of x2+bx+1=0,α+β=−b,αβ=1 We have −α−1β+−β−1α=−α+β−1β+1α=−α+β−α+βαβ=b+b=2b and, −α−1β−β−1α=αβ+2+1αβ=1+2+1=4 Thus, the equation whose roots are −α−1β and −β−1α is x2−x2b+4=0