Given polynomial is p(x) = 3×3 -5×2 – 11x – 33Put x = 3 in p(x), we get{tex} \\therefore{/tex}p(3) = 3 {tex} \\times{/tex}\xa033 – 5 {tex} \\times{/tex}\xa032 – 11 {tex} \\times{/tex}\xa03 – 3 = 81 – 45 – 33 – 3 = 0Put x = -1 in p(x), we getp(-1) = 3 {tex} \\times{/tex}\xa0(-1)3 – 5\xa0{tex} \\times{/tex} (-1)2 -11 {tex} \\times{/tex}\xa0(-1) – 3 = – 3 – 5 + 11 – 3 = 0Put x = {tex}- \\frac { 1 } { 3 }{/tex} in p(x), we getand,\xa0{tex} p \\left( – \\frac { 1 } { 3 } \\right){/tex}={tex} 3 \\times \\left( – \\frac { 1 } { 3 } \\right) ^ { 3 } – 5 \\times \\left( – \\frac { 1 } { 3 } \\right) ^ { 2 } – 11 \\times \\left( – \\frac { 1 } { 3 } \\right) – 3{/tex}={tex} – \\frac { 1 } { 9 } – \\frac { 5 } { 9 } + \\frac { 11 } { 3 } – 3{/tex}= 0\xa0So, 3,-1 and\xa0{tex} -\\frac 13{/tex}\xa0are the zeros of polynomial p(x).Let,\xa0{tex} \\alpha = 3 , \\beta = – 1 \\text { and } \\gamma = – \\frac { 1 } { 3 }{/tex} .Then,{tex} \\alpha + \\beta + \\gamma{/tex} ={tex} 3 – 1 – \\frac { 1 } { 3 } = \\frac { 5 } { 3 }{/tex}, and\xa0{tex} – \\frac { \\text { Coefficient of } x ^ { 2 } } { \\text { Coefficient of } x ^ { 3 } } = – \\left( \\frac { – 5 } { 3 } \\right) = \\frac { 5 } { 3 }{/tex}{tex} \\therefore \\quad \\alpha + \\beta + \\gamma = – \\frac { \\text { Coefficient of } x ^ { 2 } } { \\text { Coefficient of } x ^ { 3 } }{/tex}{tex} \\alpha \\beta + \\beta \\gamma + \\gamma \\alpha{/tex} = {tex} 3 \\times ( – 1 ) + ( – 1 ) \\times \\left( – \\frac { 1 } { 3 } \\right) + \\left( – \\frac { 1 } { 3 } \\right) \\times 3{/tex}=\xa0{tex} – 3 + \\frac { 1 } { 3 } – 1 = – \\frac { 11 } { 3 }{/tex}and,\xa0{tex} \\frac { \\text { Coefficient of } x } { \\text { Coefficient of } x ^ { 3 } } = – \\frac { 11 } { 3 }{/tex}{tex} \\therefore \\quad \\alpha \\beta + \\beta \\gamma + \\gamma \\alpha = \\frac { \\text { Coefficient of } x } { \\text { Coefficient of } x ^ { 3 } }{/tex}{tex} \\alpha \\beta \\gamma = 3 \\times ( – 1 ) \\times \\left( – \\frac { 1 } { 3 } \\right) = 1{/tex}……… (i)And,\xa0{tex} – \\frac { \\text { Constant term } } { \\text { Coefficient of } x ^ { 3 } } = – \\left( \\frac { – 3 } { 3 } \\right) = 1{/tex} …….. (ii)From (i) and (ii){tex} \\therefore \\quad \\alpha \\beta \\gamma = – \\frac { \\text { Constant term } } { \\text { Coefficient of } x ^ { 3 } }{/tex}