Find the roots of the quadratic equation x^2 + 7x + 12 = 0.

The roots of x^2 + 7x + 12 = 0 are -3 and -4.

To find the roots of a quadratic equation in the form ax^2 + bx + c = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 7, and c = 12. Substituting these values into the quadratic formula, we get:

x = (-7 ± √(7^2 - 4(1)(12))) / 2(1)

Simplifying under the square root:

x = (-7 ± √(49 - 48)) / 2

x = (-7 ± 1) / 2

So the two roots are:

x = (-7 + 1) / 2 = -3

x = (-7 - 1) / 2 = -4

Therefore, the roots of x^2 + 7x + 12 = 0 are -3 and -4. We can check this by substituting these values back into the original equation and verifying that they make it true.