What do you understand about the zero product property?

Question

How is the concept of zero-products applied in order to solve quadratic equations?

Describe the four steps in solving quadratic equations?

Answer 1

The Zero Product property, sometimes also called the "Zero Divisor" property, says that The product of two or more numbers is zero if and only if at least one of the numbers is zero.

In other words, a₁ * ... * a_n = 0 ↔ a_k = 0 for some k.

For example, in the equation (x - 1)(x + 3)(x - 2)(x + 4) = 0, you can conclude

x - 1 = 0 or x + 3 = 0 or x - 2 = 0 or x + 4 = 0, so that

x = 1 or x = -3 or x = 2 or x = -4.

When factoring a quadratic, you will get only two factors, both linear.

Let's do an example: 2x² - 5x + 3 = 0

We can factor it by splitting b = -5 as a sum of two numbers whose product is ac = 2*3 = 6.

You get

2x² - 2x - 3x + 3 = 0

2x(x - 1) - 3(x - 1) = 0

(2x - 3)(x - 1) = 0

2x - 3 = 0 or x - 1 = 0

x = 3/2 or x = 1