Question

If `x = (-1)/2`, is a root of the quadratic equation 3x² + 2kx + 3 = 0, find the value of k.

Answer 1

Given: `x = (-1)/2` is a root of 3x² + 2kx + 3 = 0.

Step-wise calculation:

1. Substitute `x = (-1)/2` into the equation.

2. `3(-1/2)^2 + 2k(-1/2) + 3 = 0`

⇒ `3(1/4) - k + 3 = 0`

⇒ `3/4 - k + 3 = 0`

⇒ `15/4 - k = 0`

⇒ `k = 15/4` (which is 3.75).