Find the variable value or factors of   `alpha^2 - beta^2`

If alpha and beta are the roots of x^(2)-(a-2)x-(a+1)=0 where a is a variable then the least value of alpha^(2)+beta^(2)

If alpha and beta are the roots of the equation x^(2) -x+7=0 , then find the value of alpha^(2) + beta^(2) .

If for one quadratic equation alpha + beta =5 " and " alpha beta =6 , then find 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

If alpha , beta roots of the equations x^(2) - 5x + 6 = 0 , find the value of alpha^(2) - beta^(2) .

If sin alpha+sin beta=2 then find the value of cos^(2)alpha+cos^(2)beta

If alpha and beta are zeros of y^(2)+5y+m , find the value of m such that (alpha+beta)^(2)-alphabeta=24

Let alpha_1 and alpha_2 be two real values of alpha for which the numbers 2alpha^2,alpha^4,24 taken in that order form an arithmetic progression, If beta_1 and beta_2 are two real values of beta for which the number 1,beta^2,6-beta^2 taken in the order form a geometric progression, then find the value of (alpha_1^2+alpha_2^2+beta_1^2+beta_2^2).