If `alpha,beta` are the roots of the equation `ax^2+bx+c=0` and `S_n=alpha^n+beta^n` then evaluate `|[3, 1+s_1, +s_2] , [1+s_1, 1+s_2, 1+s_3] , [1+s_2, 1+s_3, 1+s_4]|`

If alpha, beta are the roots of the equation ax^(2)+bx+c=0 and A_(n)=alpha^(n)+beta^(n) , then aA_(n+2)+bA_(n+1)+cA_n is equal to

If alpha and beta are the roots of the equation ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =

If alpha, beta are the roots of x^(2)-3x+1=0 , then the equation whose roots are (1/(alpha-2),1/(beta-2)) is

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > beta) then find the value of f(alpha,beta)=(beta^3)/2csc^2(1/2tan^(- 1)(beta/alpha))+(alpha^3)/2sec^2(1/2tan^- 1(alpha/beta))

If alpha an beta are roots of ax^(2)+bx+c=0 the value for lim_(xto alpha)(1+ax^(2)+bx+c)^(2//x-alpha) is

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If S_n=cos^ntheta+sin^n theta then find teh value of 3S_4-2S_6

if alpha,beta,gamma are the roots of x^3-3x^2 +3x + 7 =0 then (alpha-1)/(beta-1)+(beta-1)/(gamma-1)+(gamma-1)/(alpha-1)

The area between the parabolas y^2 = 4x and x^2 =4y divide the square formed by the lines x=4 , y=4 and oxes into three parts . If the area of these three parts from uppar to bottom is S_1 ,s_2 and S_3 then S_1 : S_2 :s_3 =..........