Use the zero product property to find the solutions to the equation x² - x - 6 = 0.

Solution:

Zero product property, also known as zero product principle states that if p × q = 0 , then p = 0 or q = 0 or both p = 0 and q = 0 .

Given: Linear equation is x² - x - 6 = 0

By splitting the middle term

x² - 3x + 2x - 6 = 0

Taking out the common terms

x(x - 3) + 2(x - 3) = 0

So we get,

(x - 3)(x + 2) = 0

By zero product property,

x - 3 = 0 or x + 2 = 0

x = 3 or x = -2

Therefore, the solution is 3 or -2.

Use the zero product property to find the solutions to the equation x² - x - 6 = 0.

Summary:

Using the zero product property, the solutions to the equation x² - x - 6 = 0 is 3 or -2.