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

Now,

(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 = 0Factor out x:

x(x^2 − 36) = 0x^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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