Question 1022596
For the function above, a = k+1, b = 4k, and c = 2

a.  The discriminant is {{{b^2 - 4ac = (4k)^2 - 4(k+1)2 = 16k^2 - 8k - 8}}}

c.  There will be two distinct real roots if {{{16k^2 - 8k - 8 > 0}}}.  Solving this inequality gives a solution of ({{{-infinity}}},-1/2)u(1,{{{infinity}}}).

d.  There will be two complex roots (conjugates of each other) if {{{16k^2 - 8k - 8 < 0}}}.  The solution will be the open interval (-1/2, 1).

e.  There will be a unique solution if the discriminant is EQUAL to zero.  Hence k = -1/2 or 1.