" If "S_(r)=alpha^(r)+beta^(r)+gamma^(r)" then show that "|[S_(0),S_(1),S_(2)],[S_(1),S_(2),S_(3)],[S_(2),S_(3),S_(4)]|=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(0),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(2),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

If alpha,beta are the roots of x^(2)+x+1=0 , and s_(n)=alpha^(n)+beta^(n) , then |[3,1+S_(1),1+S_(2)],[1+S_(1),1+S_(2),1+S_(3)],[1+S_(2),1+S_(3),1+S_(4)]|=?

Show that |[1,alpha,alpha^2],[1,beta,beta^2],[1,gamma,gamma^2]|=(alpha-beta)(beta-gamma)(gamma-alpha)

[ Let alpha,beta be the roots of x^(2)-2x+5=0 and let S_(n)=alpha^(n)+beta^(n) for ngt=1, then the value of |[3,1+S_(2),1+S_(3)1+S_(2),1+S_(4),1+S_(5)1+S_(3),1+S_(5),1+S_(6)]| is equal to [ (1) -12544, (2) 12544 (3) -4704, (4) -4712]]

If P is any point on ellipse with foci S_(1)&S_(2) and eccentricity is (1)/(2) such that /_PS_(1)S_(2)=alpha,/_PS_(2)S_(1)=beta,/_S_(1)PS_(2)=gamma then cot((alpha)/(2)),cot((gamma)/(2)),cot((beta)/(2)) are in

If alpha, beta , gamma are the roots of x^(3) - px^(2) + qx - r = 0 then match the following. (1)/(alpha) + (1)/(beta) + (1)/(gamma)" "(a)(p^(2) - 2q)/(r^(2)) ii. (1)/(alpha beta) + (1)/(beta gamma) + (1)/(gamma alpha)=" "(b) (q^(2) - 2pr)/(r^(2)) iii. (1)/(a^(2)) + (1)/(beta^(2)) + (1)/(gamma^(2)) =" " (c ) (p)/(r ) iv. (1)/(alpha^(2) beta^(2)) + (1)/(beta^(2) gamma^(2) ) + (1)/(gamma^(2) alpha^(2)) = " " (d) (q)/(r )