If the product of the roots of the equation $$\,{x^2} - 3\,k\,x + 2\,{e^{2lnk}} - 1 = 0\,\,\,\,is\,7$$, then the roots are real for k = .................................

If a < b < c < d, then the roots of the equation (x - a) (x - c) + 2 ( x - b) (x - d) = 0 are real and distinct.

The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has

If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval