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The roots of the quadratic equation 2x^2 - 3x - 5 = 0 are to be found.

To find the roots of a quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Here, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / 2(2)

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

Simplifying further, we get:

x = (3 + 7) / 4 or x = (3 - 7) / 4

x = 5/4 or x = -1/2

Therefore, the roots of the quadratic equation 2x^2 - 3x - 5 = 0 are x = 5/4 and x = -1/2. We can check our answer by substituting these values back into the original equation and verifying that they satisfy it.

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