If the roots of equation `x^3+a x^2+b=0a r ealpha_1,alpha_2` and `alpha_3(a ,b!=0)` , then find the equation whose roots are `(alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)`

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)) .

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 alpha!=beta but alpha^(2)=5 alpha-3,beta^(2)=5 beta-3, then find the equation whose roots are (alpha)/(beta) and (beta)/(alpha)

If alpha!=beta and alpha^(2)=5 alpha-3 and beta^(2)=5 beta-3. find the equation whose roots are alpha/ beta and beta/ alpha .

Find the coefficient of alpha^(6) in the product (1+alpha+alpha^(2))(1+alpha+alpha^(2))(1+alpha+alpha^(2)+alpha^(3)) (1+alpha)(1+alpha)(1+alpha) .

If alpha1=beta but alpha^(2)=2 alpha-3;beta^(2)=2 beta-3 then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) is

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_(2)