If `alpha, beta (alpha lt beta)` are the real roots of equation `x^(2)-(k+4) x + k^(2)-12=0` such that `4in (alpha, beta)` then find the values of k.

If alpha and beta are the roots of the equation x ^(2) + alpha x + beta = 0, then

If alpha and beta are the roots of the equations x^(2) - 6x +a=0 and satisfy the relations 3 alpha + 2 beta= 16 , then the value of a is :

If alpha and beta are the roots of the equation x ^(2) + 3x - 4 = 0 , then (1)/(alpha ) + (1)/(beta) is equal to

If alpha, beta are the roots of the quadratic equation x^(2)-2(1-sin 2theta) x-2 cos^(2) 2 theta=0, (theta in R) then find the minimum value of (alpha^(2)+beta^(2)) .

If alpha and beta are the roots of the equation x^(2)-7x+1=0 , then the value of 1/(alpha-7)^(2)+1/(beta-7)^(2) is :

Let alpha and beta be the roots of the equation px^(2) + qx + r=0 . If p, q, r in AP and alpha+beta =4 , then alpha beta is equal to