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What is zero product property

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The “Zero Product Property” says that: If a × b = 0 then a = 0 or b = 0. (or both a=0 and b=0) It can help us solve equations. The zero product property, also called zero-product principle, states that for any real numbers a and b, if ab = 0, then either a equals zero, b equals zero. In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, {\displaystyle {\text{if }}ab=0, {\text{ then }}a=0{\text{ or }}b=0.}.


The Zero Product Property – Table of Contents


If you are unable to find two terms, it’s possible you have a quadratic with no or infinitely many solutions! The zero-product property is what allows us to find the zeroes of a polynomial by factoring it. This video by GVSUmath explains the zero product property. We use this property when we solve quadratic equations. This is because factoring the equation gives us two expressions that multiply to zero.

We can set each factor equal to zero and solve for x. We’ll solve it by setting each part equal to 0. Select all correct answers. This property lets us solve factored quadratics set equal to 0.

Algebra 1 Solving Quadtradics by Factoring. Go to Topic. Let us check more about it through examples, FAQs. Zero product property has one side of the expression equal to zero and the other side is the product of two or more factors. This property applies to multiplication in algebra, in matrices, and for vectors. The zero product property says that if the product of two or more factors is equal to zero then at least one of the factors is equal to 0 because otherwise, the product won’t be equal to 0.

The zero product property can be further extended to more factors and it looks like below in that case. Note that, more than one of the factors may also be equal to zero for the product to be 0. The application of zero product property can be done for equations , but cannot be applied to matrices and vectors. Zero product property for equations is helpful to solve the equation and find the values of the variables.

The algebraic expression following the zero product property has factors and can also be solved to find the values of the variables. Zero product property is very helpful in solving the quadratic equations that are in the factored form. Similarly, the zero product property can be applied to polynomial equations. The zero product property is not applicable for matrices.

Consider the following example. The zero product property cannot be applied for vectors as well. Whenever the dot product or cross product of any two vectors is 0, it doesn’t mean that at least one of the vectors is a zero vector. In general, a ring which satisfies the zero-product property is called a domain. Thus, one can use factorization to find the roots of a polynomial. From Wikipedia, the free encyclopedia. For the product of zero factors, see empty product.

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