If one root of the equation $i x^2 - 2(i + 1) x + (2 - i) = 0$ is $(2 - i)$,then the other root is

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 3x + 5 = 0$,then find the quadratic equation whose roots are $(\alpha^2 - 3\alpha + 7)$ and $(\beta^2 - 3\beta + 7)$.

If the product of the roots of the equation $x^2+4kx+12e^{3\log k}-1=0$ where $k>0$ is $323$,then the sum of its roots is:

If the difference between the roots of the equation $x^2 + ax + b = 0$ is equal to the difference between the roots of the equation $x^2 + bx + a = 0$ $(a \neq b)$,then:

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity,then $b + c$ is equal to

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is