use the zero product property to find the solutions to the equation $x^{2}-15x - 100 = 0$.\n$x=-20$ or $x =…

use the zero product property to find the solutions to the equation $x^{2}-15x - 100 = 0$.\n$x=-20$ or $x = 5$\n$x=-20$ or $x=-5$\n$x=-5$ or $x = 20$\n$x = 5$ or $x = 20$

use the zero product property to find the solutions to the equation $x^{2}-15x - 100 = 0$.\n$x=-20$ or $x = 5$\n$x=-20$ or $x=-5$\n$x=-5$ or $x = 20$\n$x = 5$ or $x = 20$

Answer

Explanation:

Step1: Factor the quadratic equation

We need to factor (x^{2}-15x - 100=0). We look for two numbers that multiply to (- 100) and add up to (-15). The numbers are (-20) and (5). So, (x^{2}-15x - 100=(x - 20)(x+5)=0).

Step2: Apply the zero - product property

The zero - product property states that if (ab = 0), then either (a = 0) or (b = 0). So, if ((x - 20)(x + 5)=0), then (x-20=0) or (x + 5=0). Solving (x-20=0) gives (x = 20), and solving (x + 5=0) gives (x=-5).

Answer:

C. (x=-5) or (x = 20)