Roots of cubic equations are 1 and 2+√5. Since, 2+√5 is root, then its conjugate also become roots, i.e. 2−√5 is root of cubic equation. ∴ Roots =1,2+√5,2−√5 i.e. α,β,γ Let cubic equation be x3+bx2+cx+d=0 Then, Sum of Roots =−b=1+2+√5+2−√5=5 ⇒b=−5 Product of Roots =−d=(1)(2+√5)(2−√5)=4−5=−1 ⇒d=1 ∴αβ+βγ+γα=c (1)(2+√5)+(2+√5)(2−√5)+(2−√5)(1)=c ⇒2+√5+2−√5+4−5=6 ⇒3=c ∴ Cubic equation is x3−5x2+3x+1=0