find the value of k for which 3x² + 2x + k = 0 has real roots?

 if the equation should have real roots then b2 - 4ac  ≥ 0

a = 3, b = 2, c = k

then, (2)2 - 4(3)(k)≥0

4 - 12k ≥ 0

4 ≥ 12k

1/3 ≥ k

so the value of k can be any value less than or equal to 1/3.......