If α and β are the roots of the equation x2+px+q=0and the sum(α+β)x-(α2+β2)2x2+(α3+β3)3x3-….... exists, then it is
log(x2+px+q)
log(x2–px+q)
log(1+px+qx2)
log(1–px+qx2)
Explanation for the correct option:
Find the sum (α+β)x-(α2+β2)2x2+(α3+β3)3x3-….... :
Given that α and β are the roots of the equation x2+px+q=0.
⇒(α+β)=-p;α.β=q
and also given the sum (α+β)x-(α2+β2)2x2+(α3+β3)3x3-…....exists.
(α+β)x-(α2+β2)2x2+(α3+β3)3x3-…....=αx-α22x2+α33x3-.........+βx-β22x2+β33x3-.........=log(1+αx)+log(1+βx)=log(1+x(α+β)+αβx2)=log(1-px+qx2)
Hence, the correct option is D.