If  α,β,γ are the roots of 2x3−2x−1=0, then ∑α2β2=

The given equation is 2x3−2x−1=0, α,β,γ  are the roots of the equationSum of the roots : α+β+γ=0Sum of the product of two roots taken two at a time  : αβ+βγ+γα=−1Product of the roots : αβγ=12∴∑α2β2=(∑αβ)2−2αβγ∑α                               (∵ a2b2+b2c2+c2a2=(ab+bc+ca)2−2abc(a+b+c))                      =(−1)2−2(12)(0)                    =1