We have, x5−8x4+25x3−38x2+28x−8=0 Let f(x)=x5−8x4+25x3−38x2+28x−8 f(2)=32−128+200−152+56−8 f(2)=0⇒f′(x)=5x4−32x3+75x2−76x+28 f′(2)=80−256+300−152+28⇒f′(2)=0 f′(x)=20x3−96x2+150x−76 f′(2)=160−384+300−76⇒f′(2)=0 f′(x)=60x2−192x+150 f′(2)=240−384+150=6⇒f−1(2)≠0 ∴ Given, α is a root of multiplicity 3 ∴α=2⇒α2−5α+6=4−10+6=0