If the line `x=alpha` divides the area of region `R={(x , y)R^2: x^3lt=x ,0lt=xlt=1}` into equal parts, then: `2alpha^4-4alpha^2+1=0` `alpha^4+4alpha^2-1=0` `0

If the line x= alpha divides the area of region R={(x,y)in R^(2): x^(3) le y le x ,0 le x le 1 } into two equal parts, then

If the line x = alpha divides the area of region R = {(x,y) in R^(2) : x^(0) le y le x, 0 le x le 1} into two equal parts, then

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

If alpha is a root of the equation 4x^(2)+2x-1=0 then the other root is given by O -2 alpha-1 O 4 alpha^(2)+alpha-1 O 4 alpha^(3)-3 alpha O 4 alpha^(2)-3 alpha

Consider the equation 3x^2 +4x - 5 = 0 , if alpha,beta are the roots, then 1/alpha + 1/beta =

If alpha be a root of the equation, 4 x^2 + 2x - 1 =0 , then 4 alpha^3 - 3 alpha is other root.

If alpha,beta are the roots of x^(2)+x+3=0 then 5 alpha+alpha^(4)+alpha^(3)+3 alpha^(2)+5 beta+3=

Let alpha be a root of the equation x ^(2) + x + 1 = 0 and the matrix A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] then the matrix A ^( 31 ) is equal to :

If alpha is a root of the equation 4x^(2)+2x-1=0 and f(x)=4x^(2)-3x+1 , then 2(f(alpha)+(alpha)) is equal to