α,β are the roots of the equation x2−2x+3=0 . Then  the equation whose roots are P=α3−3α2+5α−2 and Q=β3−β2+β+5 is

Given α,β are roots of equation x2−2x+3=0⇒ α2−2α+3=0 -----(1) 3=-α2+2α -----(2)from eq1∴     α2=2α−3 multiply by α we get  α3=2α2−3αsub from eq 2∴  P    =2α2−3α−3α2+5α−2     =−α2+2α−2=3−2=1    and  β2−2β+3=0  ----(3)β3-2β2+3β=0β3=2β2-3β ----(4)Similarly Q=β3-β2+β+5sub from eq 4Q=2β2-3β-β2+β+5=β2-2β+5=-3+5=2  from eq 3P=1 , Q=2So, sum of roots = 3, and product of roots = 2. Then required equation is x2−3x+2=0 .