Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:

2x² — 5x — 3 = 0

Without solving, determine whether the following equations have real roots or not. If yes, find them:

Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:

2x²— 6x + 3 = 0

Find the value of k for which the quadratic equation

4x² — 2 (k + 1) x + (k + 4) = 0 has equal roots.

Find the value of k, so that the quadratic equation

(k + 1) x² – 2 (k — 1) x + 1 = 0 has equal roots.