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Let 1+sum(r=1)^(10)(3^r.^(10)Cr+r.^(10)C...

Let `1+sum_(r=1)^(10)(3^r.^(10)C_r+r.^(10)C_r)=2^(10)(alpha. 4^5+beta)` where `alpha,beta in N` and `f(x)=x^2-2x-k^2+1.` If `alpha,beta` lies between the roots of `f(x)=0` , then find the smallest positive integral value of `kdot`

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