If `|x + 2||x + 3| = alpha^2+ 5alpha – 6`, then integral values of `alpha` satisfying the equation -

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

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

The number of all possible positive integral values of alpha for which the roots of the quadratic equation 6x^2-11x+alpha=0 are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

The number of all possible positive integral values of alpha for which the roots of the quadratic equation 6x^2-11x+alpha=0 are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

The number of all possible positive integral values of alpha for which the roots of the quadratic equation 6x^2-11x+alpha=0 are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

The number of all possible positive integral values of alpha for which the roots of the quadratic equation 6x^(2)-11x+alpha=0 are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

If alpha,beta and gamma are the roots of equation x^(3)-3x^(2)+x+5=0 then y=sum alpha^(2)+alpha beta gamma satisfies the equation

The number of integral values of alpha for which the quadratic expression alpha x^(2)+|2 alpha-3|x-6 is positive for exactly two integral values of x is equal to

Roots of the equation 3x^2 -6x+4=0 are alpha and beta then find the value of alpha^2 beta + alpha beta^2

If alpha and beta are zeroes of polynomial p(x) = x^(2) - 5x +6 , then find the value of alpha + beta - 3 alpha beta