To solve the equation x² – 6 = 0 using the zero product property, we first want to rearrange the equation into a product equal to zero.
We can rewrite the equation as:
x² = 6
Next, we take the square root of both sides:
x = ±√6
Thus, the solutions to the equation x² – 6 = 0 are:
x = √6 and x = -√6.
In conclusion, by applying the zero product property, we’ve found that the equation has two solutions that are both irrational numbers, derived from the basic properties of squares and roots.