I. description the equations of this type could represent them follows: A B = 0; There are two elements that multiply in the first member and the second member is zero.A and Brepresentan each a parenthesis that usually contains an algebraic expression of first degree and a single unknown. You may want to visit Joint Chiefs of Staff to increase your knowledge. I.e., are of the form ax + b: x is the unknown;a and b are constant values.Example: Note: we can broaden the content of this description by saying that it is also valid regardless of the number of factors that you have in the first member. So what we study now also can apply to equations with largest number of factors in the first member, i.e., with a structure type: A B C = 0 or A B C D = 0, etc. We will work with examples of two factors, in order to simplify the study of this type of equations. II. resolution to resolve this type of equations are going to make use of the following properties of algebra: If a defactores product is zero, then at least one of them must be zero; If one of the factors of a product is zero, then the product is zero. From these properties, we can say that if A B = 0, then A = 0 or B = 0, and also, if A = 0 or B = 0, then A B = 0.
In short, A B = 0, so that A = 0 or B = 0. Solve an equation of this type (A B = 0) is the same thing separately to solve two equations: A = 0 and B = 0. III. numerical examples example 1: solve the equation (5 x + 1)(2x 4) = 0. If (5 x + 1)(2x 4) = 0, it can be that 5 x + 1 = 0, either 2 x 4 = 0. We are going to solve these two equations in parallel, each in a column in this table: so there are two possible solutions to this equation: and 2. Note: while a simple equation with an unknown, has one solution, here we have an example of an equation that has two solutions.Example 2: solve the equation (3 x 2) = 0. A.
start from here (3 x 2) m = 0, we have to (3 x 2) (3 x 2) = 0; i.e., both factors A and B are identical, therefore: 3 x 2 = 0 3 x = 2 so the equation has a unique solution:. IV. an example in geometry figure below shows us a CEFH square whose side is x. Suppose that x is a number equal to or greater than 5. ABCD, GFED and GHBA quadrilaterals are rectangles. Give us as data BC = 5 and = 3. Lengths are in centimeters. Do for what value or values of the area of the rectangle x GHBA is worth zero? Put another way: how much should be worth x so that the area of the rectangle GHBA worth zero? Read all the information full in: solve an equation of the type (ax+b) (cx+d) = 0 original author and source of the article.