If the roots of the equation `frac{alpha}{x-alpha}+frac{beta}{x-beta}=1` be equal in magnitude but opposite in sign , then `alpha+beta` is equal to

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

If alpha, beta in C are distinct roots of the equation x^2+1=0 then alpha^(101)+beta^(107) is equal to

If alpha and beta are the roots of the equation x^(2)+x+c=0 such that alpha+beta, alpha^(2)+beta^(2) and alpha^(3)+beta^(3) are in arithmetic progression, then c is equal to

Let alpha and beta be two roots of the equation x^(2) + 2x + 2 = 0 . Then alpha^(15) + beta^(15) is equal to

If alpha and beta are the roots of the equation x^2+sqrt(alpha)x+beta=0 then the values of alpha and beta are -

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

The roots of the equation ax^(2)+bx+c=0 are alpha and beta . Form the quadratic equation whose roots are alpha+(1)/(beta) and beta+(1)/(alpha) .

If cos( alpha+beta) + sin(alpha-beta) = 0 and 2010tan beta - 1 = 0 then tan alpha is equal to

If alpha , beta, gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If alpha and beta are the roots of the equation x^(2)+alpha x+beta=0 such that alpha ne beta , then the number of integral values of x satisfying ||x-beta|-alpha|lt1 is