It won't be sufficient to just state that (3k + 5)² - 4(1)(-3) > 0 . Further working needs to be shown to justify it.


Discriminant

= (3k + 5)² - 4(1)(-3)
= (3k + 5)² + 12

Now,

(3k + 5)² ≥ 0 for all real k
(The square of any real value is either 0 or positive)


So (3k + 5)² + 12 ≥ 12
→ (3k + 5)² + 12 > 0

Since the discriminant > 0 for all real k , the roots of the equation are always real (and distinct).

Ah yes i agree you have to show the full step thats my bad