To solve the quadratic equation x² + 7x + 12 = 0, we can factor it or use the quadratic formula. In this case, factoring is straightforward.
First, we need to look for two numbers that multiply to 12 (the constant term) and add up to 7 (the coefficient of x). The numbers 3 and 4 satisfy these conditions, as 3 × 4 = 12 and 3 + 4 = 7.
Now, we can factor the equation as follows:
(x + 3)(x + 4) = 0
Next, we apply the zero-product property. This means that if the product of two factors equals zero, at least one of the factors must be zero. Therefore, we can set each factor to zero:
x + 3 = 0 or x + 4 = 0
This gives us:
- x = -3
- x = -4
So the solutions to the equation are x = -3 and x = -4.
In conclusion, the roots of the quadratic equation x² + 7x + 12 = 0 are -3 and -4.