If α,β  are the roots of x2+3x+6=0 , then the equation whose roots are α+1α,β+1β  is

The given equation is x2+3x+6=0   …. ( 1 ) α,β  are the given roots of Eq.( 1 )Sum of the  roots : α+β=−3,       Product of the roots : αβ=6 Now finding the equation whose roots are α+1α,β+1β  isSum of the  roots : α+1α+β+1β=2αβ+(α+β)αβ                                                              =12−36=96=32 Product of the roots : (α+1α)(β+1β)=1+αβ+α+βαβ=1+6−36=46=23 The required equation is  x2−x(32)+23=0    (∵  x2−(α+β)x+αβ=0) ⇒6x2−9x+4=0