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 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 the equation x^(2) + kx+ 1 = 0 " has the roots "alpha and beta , then what is the value of (alpha + beta) xx ( alpha^(-1) +beta ^(-1))

If alpha, beta are roots of x^(2)-2x-1=0 , then value of 5alpha^(4)+12beta^(3) is

If alpha and beta are the roots of 4x^(2) + 3x +7 =0 then the value of 1/alpha + 1/beta is

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

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

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha and beta are the real roots of the equation x^(2)-(k+1)x-(k+2)=0, then minimum value of alpha^(2)+beta^(2) is

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