To solve the equation x² + x – 12 = 0 using the zero product property, we first need to express the quadratic equation in a factored form.
We start by looking for two numbers that multiply to -12 (the constant term) and add to 1 (the coefficient of x). These two numbers are 4 and -3, since 4 * -3 = -12 and 4 + (-3) = 1.
Now we can factor the quadratic equation as follows:
(x + 4)(x – 3) = 0
According to the zero product property, if the product of two factors equals zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:
x + 4 = 0 or x – 3 = 0
Solving these gives us:
x + 4 = 0 ⟶ x = -4
x – 3 = 0 ⟶ x = 3
Thus, the solutions to the equation x² + x – 12 = 0 are x = -4 and x = 3.