The Zero product property states that if ab=0, then either a=0 or b=0 (or both). The product is zero only if one or more of the factors is zero.

If, a x B = 0 then a=0 or b=0  (or both a&b=0).

Few examples to explain zero product property

Example 1: Solve (x-4)(x-7) = 0

Solution: According to “Zero product principle/product” :

If (x-4)(x-7) = 0 then (x-4) = 0 or (x-7) = 0


                         (x-4) = 0 we get x = 4

                        (x-7) = 0 we get x = 7

So, we get

x= 4 , 7

Example 2: Solve x^2 +3x - 10 = 0

Solution : We have ,

                          x^2 +3x -10= 0

Now,                x^2+5x-2x-10=0 (Using Quadratic equation)

                         x(x+5)-2(x+5) = 0

(x-2)(x+5) = 0

Using the zero product principle/ product:

This means either x= 2 or  -5

Example 3: Solve x^3 = 36x

Solution :

So let’s use Standard Form and the Zero Product principle.

Bring all to the left-hand side:

x^3 − 36x = 0

Factor out x:

x(x^2 − 36) = 0

x^2 − 36 , can be factored into (x − 6)(x + 6):

x(x − 6)(x + 6) = 0

Now we can see three possible ways it could end up as zero:

x = 0, or x = 6, or x = −6

FAQ (Frequently asked questions)

What is the use of zero product property?

The zero-product property is used in all the fields of mathematics to solve real-life problems. In order to solve most of the problems in maths like algebraic equations, quadratic equations, and many more, we need to be through with the zero-product principle. So, we advise all the students to get a proper grip on this topic to understand most of the topics in mathematics to have a bright future in all fields.

what is the zero product property?

The zero-product principle also referred to as zero product property, states that for any real numbers a and b, if ab = 0, then a =0,b =0 or both zero.

Does quadratic question use zero product principle? 

Yes, we use the zero product principle to solve quadratic questions. Because we factories two expressions that multiply together to be equal to zero.

You can also learn about trigonometry and algebra.

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