If the equation `x^2+(p^2+5)x-2p=0 ( p in R)` has roots `alpha, beta` then find the minimum value of `(1-alpha)(1-beta)`

If x^(2)+(a^(2)+100)x-2a=0 (where a in R) has the roots alpha and beta, then minimum value of (1-alpha)(1-beta) is

IF alpha and beta be the roots of the equation x^2 +px -(1)/(2p ^(2))=0 where p in R , then the minimum value of alpha ^(4) + beta ^(4) =

Consider the equation x^2-5x+2=0 with roots alpha, beta , then the value of alpha+beta+alpha^(-1)+beta^(-1)=?

If alpha and beta be the roots of the equation x^(2) + px - 1//(2p^(2)) = 0 , where p in R . Then the minimum value of alpha^(4) + beta^(4) is

If alpha and beta be the roots of the equation x^(2) + px - 1//(2p^(2)) = 0 , where p in R . Then the minimum value of alpha^(4) + beta^(4) is

The roots of the equation px^(2)-2(p+1)x+3p=0 are alpha and beta . If alpha-beta=2 , calculate the value of alpha,beta and p.

If alpha and beta be the roots of the eqution x^(2) +px -1/ (2p^(2)) = 0 , where p in R . Then the minimum possible value of alpha^(2) + beta^(2) is

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

If alpha and beta are the roots of the equation x^(2)+px-(1)/(2p^(2))=0, where p in R .Then,the minimum value of alpha^(4)+beta^(4) is