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 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) + 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)

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 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)=n(alpha_1^ (n-1)+a)

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_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