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

Let `1+ sum_(r=1)^10 (3^r C(10,r) + r C(10,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 betweenm the roots of `f(x)=0` then find the smalles positive integral value of k

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