Find a quadratic equation whose product of roots `x_1 and x_2` is equal to 4 and satisfying the relation `(x_1)/(x_1-1)+(x_2)/(x_2-1) =2.`

Find the quadratic equation whose roots are the cubes of the roots of x^2-4x+3=0 .

The equation x-2/(x-1)=1-2/(x-1) has

Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2

One root of the equation x+(1)/(x)=-2 is

Let S be the set of all non-zero real numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1 and x_2 satisfying the inequality abs(x_1-x_2)lt1 . Which of the following intervals is (are) a subset(s) of S ?

The quadratic equation x^(2)-2x+1=0 have no real root.

If blt0 , then the roots x_1 and x_2 of the equation 2x^2+6x+b =0, satisfy the condition (x_1/x_2)+(x_2/x_1)ltk where k is equal to

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

If f(x)=x^2-3x+4, then the value of x which satisfy the relation f(x) = f(2x+1) are___