If the equations `2x^2+alphax+alpha=0` and `x^2+2x+2alpha=0` have acommon root then find the number of integral values of `alpha`

If the equations 2x^(2)+alpha x + alpha= 0 and x^(2)+2x+2 alpha= 0 have a common root, then find the real values of alpha .

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

If alpha,beta in R and the quadratic equations x^2+2x+7=0a n d4x^2+alphax+beta=0 have atleast one common roots, then the value of alpha+beta is

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 the equation, x^2+3x+6=0 has roots alpha, beta , then find the equation having roots alpha+beta, alpha-beta is.

Let both root of equation ax^2 - 2bx + 5 = 0 are alpha and root of equation x^2 - 2bx - 10 = 0 are alpha and beta . Find the value of alpha^2 + beta^ 2

Let both root of equation ax^2 - 2bx + 5 = 0 are alpha and root of equation x^2 - 2bx - 10 = 0 are alpha and beta . Find the value of alpha^2 + beta^ 2

If alpha and beta are the roots of the equation 2x^2+3x-6 then find the value of alpha^2+beta^2