Question 16705
3x^2 - 2x + k = 0

For imaginary roots, discriminant(D) must be less than zero.

D=b^2-4ac is the discriminant.

D= (-2)^2 -4(3)(k)
 = 4 - 12k
This must be less than zero.

Therefore, 4 - 12k < 0
4<12k
1<3k
1/3<k

Hence for all values of k which are less than 1/3,the roots will be imaginary.

<P>For k=1/3,roots will be real and equal. All values of k greater than 1/3 will result in real distinct roots.

<P>Hope this helps,
Prabhat