If then or ,where and are real numbers or algebraic expressions.Ī quadratic equation is an equation containing a second-degree polynomial for example THE ZERO-PRODUCT PROPERTY AND QUADRATIC EQUATIONS We can use the zero-product property to solve quadratic equations in which we first have to factor out the greatest common factor (GCF), and for equations that have special factoring formulas as well, such as the difference of squares, both of which we will see later in this section. We will look at both situations but first, we want to confirm that the equation is written in standard form,, where, and are real numbers, and. The process of factoring a quadratic equation depends on the leading coefficient, whether it is or another integer. If we were to factor the equation, we would get back the factors we multiplied. Set equal to zero, is a quadratic equation. For example, expand the factored expression by multiplying the two factors together. So, in that sense, the operation of multiplication undoes the operation of factoring. Multiplying the factors expands the equation to a string of terms separated by plus or minus signs. In other words, if the product of two numbers or two expressions equals zero, then one of the numbers or one of the expressions must equal zero because zero multiplied by anything equals zero. Solving by factoring depends on the zero-product property, which states that if, then or, where and are real numbers or algebraic expressions. If a quadratic equation can be factored, it is written as a product of linear terms. Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. Often the easiest method of solving a quadratic equation is factoring. They are used in countless ways in the fields of engineering, architecture, finance, biological science, and, of course, mathematics. For example, equations such as and are quadratic equations. An equation containing a second-degree polynomial is called a quadratic equation.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |