Consider `f(x)=(x^2 - 2mx – 4(m^2+1))(x^2- 4x-2m(m^2 +1))`, For `m = k, f(x)=0` has three differentreal roots, then `k` is :

Consider f(x)=(x^(2)-2mx4(m^(2)+1))(x^(2)-4x-2m(m^(2)+1)), For m=k,f(x)=0 has three differentreal roots,then k is :

The sum of all real values of 'm for which the polynomial f(x)={x^(2)-2mx-4(m^(2)+1)}{x^(2)-4x-2m(m^(2)+1)} has exactly three distinct real linear factors is

The sum of all real values of 'm' for which the polynomial f(x)={x^(2)-2mx-4(m^(2)+1)} {x^(2)-4x-2m(m^(2)+1)} has exactly three distinct real linear factors is

If m in Z and the equation m x^(2) + (2m - 1) x + (m - 2) = 0 has rational roots, then m is of the form

If the equation x^2-(2 + m)x + (m2-4m +4) = 0 has coincident roots, then

Consider the equation (log_2 x)^(2) -4 log_2 x - m^(2) - 2m -13=0 , m in R . Let the real roots the equation be x_1,x_2 such that x_1 lt x_2 . The sum of maximum value of x_1 and minimum value of x_2 is :

If the equation x^(2) - (2 + m) x + (m^(2) - 4m + 4) = 0 in x has equal roots, then the values of m are

If f(x)=2^x-x^2 and f(x)=0 has m solutions f'(x)=0 has n solutions then m+n=

Consider the equation log _(2)^(2) x -4 log _(2)x-m^(2) -2m -13=0, m in R. Let the real roots of the equation be x _(1), x _(2) such that x _(1)lt x _(2). The sum of maximum value of, x _(1) and minimum value of x _(2) is :