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

Given:

x^2 -15x -100

Use the zero product property to find the solutions of the equation.

Solution:

Before using the zero product property we must first factor out the equation. In order to do so, we take a look at the 2nd and 3rd values, then we must think of two numbers that when added the answer will -15, and when multiplied the answer is -100, if we cannot find the number, then we can use the quadratic formula.

 Quadratic Formula:

x=(−b±√(b^2 -4ac))/2a
a = 1, b = -15, and c = -100

Substitute the given values of a, b and c to the quadratic formula.

x=(−(−15)±√((−15)^2−4(1)(−100))/2(1)

x=(15±√(225−(-400)) /2

x=(15±√(225+400)) /2

x=(15±√(625) /2

x=15±25 /2

x = 15 + 25/2

x = 40/2

x = 20

x = 15 -25/2

x = -10/2

x = -5

We cannot use the zero property anymore since quadratic equations give exact solutions, and there is no need to equate the solution to 0.

Final answer:

x = 20

x= -5