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

If alpha is a roots equations 4x^2+2x-1=0andf(x)=4x^3-3x+1,then2(f(alpha)+alpha) is

If alpha is a real root of the equation x^(2)+3x-tan2=0 then cot^(-1)alpha+"cot"^(-1)1/(alpha)-(pi)/2 can be equal to

Let alpha be a root of the equation x ^(2) - x+1=0, and the matrix A=[{:(1,1,1),(1, alpha , alpha ^(2)), (1, alpha ^(2), alpha ^(4)):}] and matrix B= [{:(1,-1, -1),(1, alpha, - alpha ^(2)),(-1, -alpha ^(2), - alpha ^(4)):}] then the vlaue of |AB| is:

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

If alpha is a positive root of the equation x^4 +x^3 -4x^2 +x+1=0 then alpha +1/alpha

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

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

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha and beta are roots of the equation x^(2)+x+1=0 , then alpha^(2)+beta^(2) is equal to