Answer:

x = (√33 - 1) / 4 and x = -(√33 + 1) / 4

Step-by-step explanation:

The roots of the quadratic equation 2x² + x - 4 = 0 can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 1, and c = -4. Plugging in these values:

x = (-1 ± √(1² - 4 * 2 * -4)) / 2 * 2

x = (-1 ± √(1 + 32)) / 4

x = (-1 ± √33) / 4

So, the roots of the equation are:

x = (√33 - 1) / 4 and x = -(√33 + 1) / 4

These are the two solutions to the equation 2x² + x - 4 = 0.