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_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)

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot

If sqrt(alpha_1-1)+2sqrt(alpha_2-4)+3sqrt(alpha_3-9)+4sqrt(alpha_4-16)=(alpha_1+alpha_2+alpha_3+alpha_4)/2w h e r ealpha_1,alpha_2,alpha_3,alpha_4 are all real. Thena. alpha_1+alpha_2=10 b. alpha_2+alpha_3=26 c. alpha_4-alpha_3=12 d. alpha_4-alpha_2-alpha_1=22

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

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 alpha, beta are roots of the equation x^(2) + x + 1 = 0 , then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , is

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If alpha is nonreal and alpha= (1)^(1/5) then the find the value of 2^(|1+alpha+alpha^2+alpha^-2-alpha^-1|)

If alpha, beta are the roots of x^(2)+2x+5=0 , then the equation whose roots are (alpha+1)/(alpha), (beta+1)/(beta) is