Number of integral values of `a` for which the equation `cos^2x-sinx+a=0` has roots when `x in (0,pi/2)` is____________

The number of integral values of b, for which the equation x^(2)+bx-16=0 has integral roots, is

The value of k for which the equation x^2+kx+25=0 has equal roots is

Number of integral values of a for which the equation x^2-(a+1)x+a-1=0 , has integral roots, is equal to -

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

Find the value of k for which the equation x^2 −6x+k=0 has distinct roots.

The value of a for which the equation 2x^(2)+2 sqrt(6)x+a=0 has equal roots, is

Number of integral value(s) of m for which the equation sinx-sqrt(3)cosx=(4m-6)/(4-m) has solutions, x in [0,2pi] , is ________

Find the number of integral values of k for which the equation 7 cos x+5 sin x=2k+1 has at least one solution.

Number of values of p for which equation sin^3x+1+p^3-3p sinx=0(p >0) has a root is ________

Find the value of a if the equation 2x^2-(a+1)x+(a-1)=0 has equal roots.