**Question: Which of the following is the correct solution to the quadratic equation 4x ^ 2 – 5x – 12 = 0?**

**x = 5/8 + i√167/8**- x = 5/8 – i√167/8
- x = -3/8 + i√167/8
- x = -3/8 – i√167/8

**Answer: A) x = 5/8 + i√167/8**

**Solution:**

We can solve the quadratic equation `4x^2 - 5x - 12 = 0`

using the quadratic formula:

```
x = (-b ± √(b² - 4ac)) / 2a
```

where `a`

, `b`

, and `c`

are the coefficients of the quadratic equation.

In this case, ** a = 4, b = -5, and c = -12**. Substituting these values into the quadratic formula, we get:

```
x = (-(-5) ± √((-5)² - 4 * 4 * -12)) / 2 * 4
```

```
x = (5 ± √(225 + 192)) / 8
```

```
x = (5 ± √417) / 8
```

```
x = 5/8 ± i√167/8
```

```
```

Therefore, the correct solution to the quadratic equation `4x^2 - 5x - 12 = 0`

is `x = 5/8 + i√167/8`

.

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