[" Show that the rioots of the equation "x^(2)+px-n^(2)=0" are teal for all teal "],[" values of pand "y" ."]

Show that the roots of the equation x^(2)+px-q^(2)=0 are real for all real values of p and q.

If the equation x^(2)+9y^(2)-4x+3=0 is satisfied for all real values of x and y, then

Show that the roots of the equation x^2 -2px + p^2 - q^2 + 2qr-r^2 = 0 are rational.

Show that the equation x^2+a x-4=0 has real and distinct roots for all real values of a .

If -4 is a root of the equation x^(2)+px-4=0 and if the equation x^(2)+px+q=0 are equal roots, find the values of p and q.

If the roots of the quadratic equation x^(2) - 4x- log_(10) N= 0 are all real, then the minimum value of N is

If 2 is the root of the quadratic equation 3x^(2)+px-8=0 and 4x^(2)-2px+K=0 has equal roots, find the value of K.

If -4 is a root of the equation x^(2)+px-4=0 and the equation x^(2)+px+q=0 has equal roots, then the value of q is