Question

x^2 - 9x - 36 = 0Use zero product property. Solve for x

Answer 1

Given the Quadratic Equation:

$x^2-9x-36=0$

You need to remember that the Zero Product Property states that if:

$ab=0$

Then:

$a=0\text{ }or\text{ }b=0$

In this case, you can factor the given equation by finding two numbers whose sum is -9 and whose product is -36. These numbers are 3 and -12. Then:

$(x+3)(x-12)=0$

Based on the Zero Product Property, you know that:

$(x+3)=0\text{ }or\text{ }(x-12)=0$

Then, by solving each part by "x", you get:

$x=-3\text{ }or\text{ }x=12$

Hence, the answer is:

$x=-3\text{ }or\text{ }x=12$