Question

p(x)=t2-4t+3findalpha4beta3+alpha3beta4

Answer 1

p(x)= t^2- 4t+ 3= 0
t^2 -4t+ 3= 0
t^2- t - 3t +3= 0 {middle term split}
t (t-1) -3 (t-1) =0
(t-3) (t-1) =0
therefore, alpha= 3;  beta=1

Now, alpha^4 beta^3 + alpha^3 beta^4 = (3)^4 (1)^3 + (3)^3 1^4
                                                              = 81+27
                                                              = 108