If `sum_(n=1)^nalpha_n=a n^2+b n ,w h e r ea ,b` are constants and `alpha_1,alpha_2alpha_3 in {12,39}a n d25alpha_137alpha_2,49alpha_3` be three digit number, then prove that `|alpha_1alpha_2alpha_3 5 7 9 25alpha_1 37alpha_2 49alpha_3|=0`

If sum_(n=1)^nalpha_n=a n^2+b n ,w h e r ea ,b are constants and alpha_1,alpha_2,alpha_3 in {1,2,3,......,9}a n d25alpha_1,37alpha_2,49alpha_3 be three digit number, then prove that |alpha_1alpha_2alpha_3 5 7 9 25alpha_1 37alpha_2 49alpha_3|=0

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

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

If alpha = pi/3 , prove that cos alpha*cos 2alpha*cos 3alpha*cos 4alpha*cos 5alpha*cos 6alpha = -1/16 .

If alpha = pi/3 , prove that cos alpha*cos 2alpha*cos 3alpha*cos 4alpha*cos 5alpha*cos 6alpha = -1/16 .