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2014-12-05T12:40:41+05:30

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 given  a x² - 2 b x + c = 0
      and  α,  β  are the roots

     hence,   α + β = 2 b / a          and  αβ = c/a
      
     α³ β³ + α² β³ + α³ β² =  α² β² ( α β + β + α  )

           = (c/a)² ( c/a + 2 b/ a )

           = c² ( c + 2b) / a³

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2014-12-05T13:06:19+05:30
Ax²-2bx+c=0 and α&β are roots
From the relation
                     α+β=-2b/a and αβ=c/a
Then substituting value
                       α³β³+α²β³+α³β²=α²β²(αβ+β+α)
                                              =(c/a)²(c/a-2b/a)
                                              =c²(c-2b)/a³
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