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, 1+s_2] , [1+s_1, 1+s_2, 1+s_3] , [1+s_2, 1+s_3, 1+s_4]|`

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 roots of 375x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n), then underset(n rarr infty) sum_(r = 1)^(n) S_(r) is :

If alpha, beta are the roots of a x^(2)+b x+c=0 the equation whose roots are (alpha+beta)^(-1) , alpha^(-1)+ beta^(-1) is

If alpha , beta are roots of 375 x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n) , then underset(n rarr infty)(lim) sum_(r= 1)^(n) s_(r) is :

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 the roots of the equation (x^(2) -bx)/(ax - c) = (lambda - 1)/(lambda + 1) are such that alpha + beta =0 , then the value of lambda is :

Let 1 gm s^-1 = alpha Ns then value of alpha is

Given that alpha , gamma are roots of the equation Ax^(2) - 4x + 1 = 0 , and beta, delta 1 the equation of Bx^(2) - 6x + 1 = 0 , such that alpha , beta, gamma and delta are in H.P., then

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)