To solve the equation x² – 15x – 100 = 0 using the zero product property, we need to factor the quadratic expression. The zero product property states that if the product of two factors is zero, then at least one of the factors must be equal to zero.
First, we will rearrange the equation:
x² – 15x – 100 = 0
Next, we need to factor the quadratic. We are looking for two numbers that multiply to -100 (the constant term) and add up to -15 (the coefficient of x). After analyzing possible pairs, we find that:
- -20 and +5 multiply to -100 and add up to -15.
Therefore, we can factor the quadratic as:
(x – 20)(x + 5) = 0
Now, applying the zero product property, we set each factor equal to zero:
- x – 20 = 0
- x + 5 = 0
Solving these equations gives us:
- x = 20
- x = -5
Thus, the solutions to the equation x² – 15x – 100 = 0 are:
- x = 20
- x = -5
In conclusion, by applying the zero product property after factoring the quadratic, we can find the solutions to the equation easily.