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 :

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 :

Consider the equation log_(2)^(2)x-x-4log_(2)x-m^(2)-2m-13=0,m varepsilon R Let the real roots of the equation be x_(1),x_(2), such that x_(1)

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 < x_2 .The set of all values of m for which the equation has real roots is (i) (-infty ,0) (ii) (0,infty) (iii) [1, infty) (iv) (-infty,infty)

If m and n are the roots of the equations x^(2) - 6x+ 2 =0 then the value of (1)/(m) + (1)/( n) 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

Let x_(1) and x_(2) be the real roots of the equation x^(2)-(k-2)x+(k^(2)+3k+5)=0 then the maximum value of x_(1)^(2)+x_(2)^(2) is

If x_1 and x_2 are the solutions of the equation x^(log_(10)x)=100x such that x_1gt1 and x_2lt1 , the value of (x_1x_2)/2 is

If x_1 and x_2 are the solutions of the equation x^(log_(10)x)=100x such that x_1gt1 and x_2lt1 , the value of (x_1x_2)/2 is

If x_1 and x_2 are the solutions of the equation x^(log_(10)x)=100x such that x_1gt1 and x_2lt1 , the value of (x_1x_2)/2 is