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If `alpha,beta` are the roots of the equation `x^(2)+4x+p=0,` where `=Sigma_(r-0)^(n) ""^(n)C_(r)(1+rt)/((1+nt)^(r ))(-1)^(r )`, then `|alpha-beta|` is equal to: |
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Answer» Correct Answer - D `p=underset(r=0)overset(n)Sigma.^(n)(1+rt)/(1+nt)^(r) (-1)^(r)=` `underset(r=0)overset(n)Sigma.^(n)C_(r)((-1)/(1+nt))^(r)+ntunderset(r=0)overset(n)Sigma.^(n-1)C_(r-1)((-1)/(1+nt))^(r)` `=(1-(1)/(1+nt))^(n)-(nt)/(1+nt)underset(r=0)overset(n)sum.^(n-1)C_(r-1)((-1)/(1+nt))^(r-1)` `=((nt)/(1+nt))^(n)-(nt)/(1+nt)(1-(1)/(1+nt))^(n-1)=0` `implies x^(2)+4 x=0 implies x=0,-4implies|alpha-beta|=4` |
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