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

Find the value of a for which the equation a sin(x+pi/4)=sin2x+9 will have real solution.

The number of integral values of m for which the equation (1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0, has no real roots is

find the values k for which the quadratic equation 2x^2 + Kx +3=0 has two real equal roots

Find the value of k for which the given equation 9x^(2) + 3kx + 4 = 0 has real and equal roots.

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

Find the values of k so that the equation x^(2)-2x(1+3k)+7(3+2k)=0 has real and equal roots.

Number of integral values of a for which the equation cos^2x-sinx+a=0 has roots when x in (0,pi/2) 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 values of a for which the roots of the equation x^2+a^2=8x+6a are real.