Consider the equation `(x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=(1),` where `m` is a real parameter. By putting `x^2+x+1=t(2)` then `t >= 3/4` for real `x` the equation can be transferred to `f(t) = t^2- (m-3)t + m=0`

Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), where m is a real parameter. By putting x^2+x+1=t--(2) then t >= 3/4 for real x the equation can be transferred to f(t) = t^2- (m-3)t + m=0 . At what values of m for which the equation (1) will have real roots?

Find the equation to the locus represented by x=(2+t+1)/(3t-2), y=(t-1)/(t+1) wher t is variable parameter.

If x = (2at)/(1 + t^2) , y = (a(1-t^2) )/(1 + t^2) , where t is a parameter, then a is

Let f(x) = int_1^x sqrt(2 - t^2) dt . Then the real roots of the equation x^2 - f(x) = 0 are:

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 :

Let f(x) = int_1^x sqrt(2 - t^2)dt . Then the real roots of the equation x^2 - f' (x) = 0 are :