Zero-product Property

In the branch of mathematics called algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, it is the following assertion:

If, then either or .

The zero-product property is also known as the rule of zero product or nonexistence of zero divisors. All of the number systems studied in elementary mathematics — the integers, the rational numbers, the real numbers, and the complex numbers — satisfy the zero-product property. In general, a ring which satisfies the zero-product property is called a domain.

Read more about Zero-product PropertyAlgebraic Context, Examples, Non-examples, Application To Finding Roots of Polynomials

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Zero-product Property - Application To Finding Roots of Polynomials
... we may allow the coefficients and to come from any integral domain.) By the zero-product property, it follows that either or ... By the zero-product property, it follows that are the only roots of any root of must be a root of for some ...

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