If one root the quadratic equation 2x² + kx – 6 = 0 is 2. Find the value of "k" and also find the other root.

Given: One root of 2x² + kx – 6 = 0 is 2

Then At x = 2, the equation will be satisfied.

2 (2)² + k × 2 – 6 = 0

8 + 2 k – 6 = 0

2 k + 2 = 0

K = –1

So now the equation becomes 2x² + 2x – 6 = 0

For this equation, Product of the roots = (–6/2)

Product of roots = – 3

Let a and b be the roots of the equation and it is given that a = 2

2 × b = –3

B = –3/2

Hence the value of k = –1 and other root is –3/2.