If `alpha_1, ,alpha_2, ,alpha_n` are the roots of equation `x^n+n a x-b=0,` show that `(alpha_1-alpha_2)(alpha_1-alpha_3)(alpha_1-alpha_n)=n(alpha_1^ n-1+a)`

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha

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 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 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

If alpha be a root of equation x^2+x+1=0 then find the vlaue of (alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2

If 1,alpha_1,alpha_2, ,alpha_(n-1) are the n t h roots of unity, prove that (1-alpha_1)(1-alpha_2)(1-alpha_(n-1))=ndot Deduce that sinpi/nsin(2pi)/n sin((n-1)pi)/n=n/(2^(n-1))

If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the value of (3-alpha)(3-alpha^(2))(3-alpha^(3))……(3-alpha^(n-1)) , is

If nge3and1,alpha_(1),alpha_(2),.......,alpha_(n-1) are nth roots of unity then the sum sum_(1leiltjlen-1)alpha_(i)alpha(j)=

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

If 1,alpha_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is imaginary cube root of unity)