Given, roots of the equation x5+4x4−13x3−52x2+36x+144=0 are α1β,γ,2, and ε, where α<β<γ<2<ε Now, x5+4x4−13x3−52x2+36x+144=0 ‌⇒‌‌(x+4)(x+3)(x+2)(x−2)(x−3)=0 ‌⇒‌‌x=−4,−3,−2,2,3 ‌∴α=−4,β=−3,γ=−2‌ and ‌ε=3 Now, α+2β+3γ+5ε ‌=(−4)+2(−3)+3(−2)+5(3) ‌=−4−6−6+15 ‌=−16+15=−1