a) for REAL roots, the discriminant of the quadratic equation must be > 0
a = 1 b = (3k-1) c =10 + 2k
b^2 - 4ac >0 sub in the values above and solve for 'k' .... can you take it from here with that help?
Second part For TWO EQUAL roots the discriminat must = 0
b^2 - 4ac = 0 a b c are the same as above