Question

if alpha and bita are the roots of x2-px+q=0 then alpha3+bita3​

Answer 1

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log(1+px+qx2)  

log(1+qx+px2)

log(x2+px+q)

none of these

Solution :

Since α,β are the roots of the equation

x2−px+q=0

∴α+β=pandαβ=q

Now

(α+β)x−α2+β22x2+α3+β33x3…

=(αx−α2)x22+α3x33+(βx−β2x22+β3x33

=log(1+αx)+log(1+βx)

=log{(1+αx)(1+βx)}

log{(1+α+β)}x+αβx2}=log(1+px+qx2)

i hope it is right :)