`(x-alpha)^(2)+4(x-alpha)(-2)/(x-alpha)-3=0`

If alpha_(2)

Assertion (A ) : the roots x^4 -5x^2 +6=0 are +- sqrt(2) ,+-sqrt(3) Reason (R ) : the equation having the roots alpha_1 , alpha_2 , ….., alpha_n is (x-alpha_1) ( x- alpha_2 )…. (x-alpha_n)=0

Assertion (A ) : the roots x^4 -5x^2 +6=0 are +- sqrt(2) ,+-sqrt(3) Reason (R ) : the equation having the roots alpha_1 , alpha_2 , ….., alpha_n is (x-alpha_1) ( x- alpha_2 )…. (x-alpha_n)=0

Let |(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x)|=1/6(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4)) be an indentity in x , where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are independent of x . Then find the value of alpha_(1)alpha_(2)alpha_(3)alpha_(4) .

let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4)) be an identity in x, where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are independent of x. Then find the value of alpha_(1)alpha_(2)alpha_(3)alpha_(4)

let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4)) be an identity in x, where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are independent of x. Then find the value of alpha_(1)alpha_(2)alpha_(3)alpha_(4)

If the equation (alpha^(2)-5alpha+6)x^(2)+(alpha^(2)-3alpha+2)x+(alpha^(2)-4)=0 has more than two roots, then the value of alpha is :

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 , then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 , then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is :