Use the zero product property to find the solutions to the equation x² - 15x - 100 = 0.

Solution:

It is given that,

The zero product property must be used to find the solutions to the equation x² - 15x - 100 = 0,

Now,

Look for 2 numbers that when you multiply them, obtain the result -100 and when you add them, obtain the result -15.

Let x² - 15x - 100 = 0

x² - 20x + 5x - 100 = 0

Now, take out common terms,

x(x - 20) + 5(x - 20) = 0

(x - 20) (x + 5) = 0

Then,

Equating both the factors with 0 to calculate the value of x, we get

x - 20 = 0, x + 5 = 0

x = 20, x = -5

Therefore, the solution to the equation is x = 20 or x = - 5.

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Use the zero product property to find the solutions to the equation x² - 15x - 100 = 0.

Summary:

By using the zero product property, the solutions to the equation x² - 15x - 100 = 0 is x = 20 or x = - 5.