If 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 equationx2−2x+3=0⇒ α2−2α+3=0               (1) and  β2−2β+3=0            (2)            ⇒     α2=2α−3 or α3=2α2−3α⇒ P    =2α2−3α−3α2+5α−2          =−α2+2α−2=3−2=1                    [Using (1)]Similarly, we have Q = 2.Now, sum of roots is 3 and product of roots is 2. Hence, therequired equation is x2−3x+2=0