If `x^(2) +ax - 3x-(a+2) = 0` has real and distinct roots, then minimum value of `(a^(2)+1)//(a^(2)+2)` is

If the equation x^(2)+4x+k=0 has real and distinct roots, then find the value of 'k'.

If x^(2)-ax+b=0 where a,b in N has real and distinct roots,then a_(min)+b_(min)=

If x^(2)-4x+log_((1)/(2))a=0 does not have two distinct real roots,then maximum value of a is

If the roots of 5x^(2)-kx+1=0 are real and distinct then

If (a^(2)-14a+13)x^(2)+(a+2)x-2=0 does not have two distinct real roots, then the maximum value of a^(2)-15a is _________.

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

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

If the equation x^(4)+ax^(3)+2x^(2)+bx+1=0 has at least one real root (a ,b in R) then the minimum value of a^(2)+b^(2)

If x^(2)-ax+1=0 has two distinct roots, then value of a is precisely different from