If `alpha=cos((2pi)/7)+i sin((2pi)/7)` then a quadratic equation whose roots are `(alpha+ alpha^(2)+ alpha^(4))` and `(alpha^(3)+ alpha^(5)+alpha^(6))`

If alpha=cos(2 pi)/(7)+i sin(2 pi)/(7) then a quadratic equation whose roots are (alpha+alpha^(2)+alpha^(4)) and (alpha^(3)+alpha^(5)+alpha^(6)) is

If alpha is one of the non real imaginary seventh roots of unity, then form the quadratic equation whose roots are given by alpha + alpha^(2) + alpha^(4) and alpha^(3) + alpha^(5) + alpha^(6)

Given sin alpha=p, the quadratic equation whose roots are tan((alpha)/(2)) and cot((alpha)/(2)) is

If alpha=cos((2 pi)/(5))+i sin((2 pi)/(5)), then find the value of alpha+alpha^(2)+alpha^(3)+alpha^(4)

If alpha is an imaginary roots of x^(5)-1=0, then the equation whose roots are alpha+alpha^(4) and alpha^(2)+alpha^(3) is

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

alpha=e^((2 pi)/(5)i)then1+alpha+alpha^(2)+alpha^(3)+alpha^(4)+2 alpha^(5)=