Question

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

Answer 1

Given: 2x² + 2x + k = 0 and one root `x = (-1)/3`.

Step-wise calculation:

1. Substitute `x = (-1)/3` into the equation:

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

2. Compute terms:

`2((-1)/3)^2 = 2(1/9) = 2/9` and `2((-1)/3) = (-2)/3`

3. So, `2/9 - 2/3 + k = 0`

Convert to ninths:

`2/9 - 6/9 + k = 0` 

`(-4)/9 + k = 0`

4. Solve for k:

`k = 4/9`