Find the conditions on `alpha` and `beta` if `x_1, x_2, x_3` satisfying the cubic `x^3 - x^2 - alphax + beta = 0` are in AP.

Find alpha and beta if x+1 and x+2 are factors of p(x)=x^(3)+3x^(2)-2alphax+beta .

Find alpha\ a n d\ beta , if x+1\ a n d\ x+2 are factors of x^3+3x^2-2alphax+beta

Find alpha and beta, if x+1 and x+2 are factors of x^(3)+3x^(2)-2 alpha x+beta

The real numbers x_1, x_2, x_3 satisfying the equation x^3-x^2+beta x+gamma=0 are in A.P. Find the intervals in which beta and gamma lie.

find alpha and beta if (x+1) and (x+2) are factors x^3+3x^2-2alphax+beta

If alpha and beta are the roots of the equation 3x^(2)+7x+3=0 Find the value of alpha beta:

Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisfy the equatin x ^(3) -3x ^(2)+4x-5=0,alpha, beta in R, then alpha + beta =

Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisfy the equatin x ^(3) -3x ^(2)+4x-5=0,alpha, beta in R, then alpha + beta =

If alpha, beta, 1 are the roots of x ^(3) - 2x ^(2) - 7x + 6 =0, then find alpha, beta.

If alpha and beta is the root of the equation x^2-3x+2=0 then find the value of alpha^2 + beta^2