Find the values of k for each of the following quadratic equations, so that they have two equal roots.

We know that if an equation ax² + bx + c = 0 has two equal roots,

its discriminant

(b² − 4ac) will be 0.

(I) 2x² + kx + 3 = 0

Comparing equation with ax² + bx + c = 0, we obtain,

a = 2, b = k, c = 3

Discriminate = b² − 4ac = (k)²− 4(2) (3) = k² − 24

For equal roots,

Discriminant = 0

k² − 24 = 0

k² = 24