If `alpha_(1)`, `alpha_(2)`, `alpha_(3)`, `alpha_(4)` are the roots of the equation `3x^(4)-(l+m)x^(3)+2x+5l=0` and `sum alpha_(1)=3` , `alpha_(1)alpha_(2)alpha_(3)alpha_(4)=10` then `(l,m)`

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If 1,alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the fifth roots of unity then sum_(i=1)^(4)(1)/(2-alpha_(i))=

If alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________

If alpha_(1),alpha_(2)...alpha_(6) are the roots of the equation x^(6)-12x^(5)+ax^(4)-bx^(3)+cx^(2)-dx+64=0 then b equals

If alpha_(1),,alpha_(2),...,alpha_(n) are the roots of equation x^(n)+nax-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(2))...(alpha_(1)-alpha_(n))=n(alpha_(1)^(n-1)+a)

If alpha_(1),alpha_(2),alpha_(3)......alpha_(n) are roots of the equation f(x)=0 then (-alpha_(1),-alpha_(2),-alpha_(3),......alpha_(n)) are the roots of

If alpha_(1),alpha_(2),alpha_(3),.........,alpha_(n) are the roots of f(x)=0 then the equation whose roots (alpha_(1))/(K),(alpha_(2))/(K),(alpha_(3))/(K),.........(alpha_(n))/(K) is where , K!=0

If alpha,beta are the roots of the quadratic equation 4x^(2)-4x+1=0 then alpha^(3)+beta^(3)=