solving a quadratic equation by factoring

#Solving a quadratic equation by factoring how to
#Solving a quadratic equation by factoring plus

However, it might be easier to factor in some cases to avoid radicals and fractions in the quadratic formula. Of course, the quadratic formula will work for any quadratic equation you choose. If factoring is hard, the quadratic formula (a shortcut for completing the square) helps.

Graphing gives a good visual, but it is hard to find values of x from a graph with no equation. So, how do you solve quadratic equations? You can solve quadratic equations by graphing, factoring, completing the square, & the quadratic formula. Luckily, there are several ways to do it.

#Solving a quadratic equation by factoring how to

Quadratic equations come up often in mathematics and physics, and it is vital to know how to solve them. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. We can use the methods for solving quadratic equations that we learned in this section to solve for the missing side. Because each of the terms is squared in the theorem, when we are solving for a side of a triangle, we have a quadratic equation. We use the Pythagorean Theorem to solve for the length of one side of a triangle when we have the lengths of the other two. It has immeasurable uses in architecture, engineering, the sciences, geometry, trigonometry, and algebra, and in everyday applications. It is based on a right triangle, and states the relationship among the lengths of the sides as a 2 + b 2 = c 2, a 2 + b 2 = c 2, where a a and b b refer to the legs of a right triangle adjacent to the 90° 90° angle, and c c refers to the hypotenuse. One of the most famous formulas in mathematics is the Pythagorean Theorem. As 100 100 is a perfect square, there will be two rational solutions.ī 2 − 4 a c = ( −5 ) 2 − 4 ( 3 ) ( −2 ) = 49. For example, expand the factored expression ( x − 2 ) ( x + 3 ) ( x − 2 ) ( x + 3 ) by multiplying the two factors together.Ĭalculate the discriminant b 2 − 4 a c b 2 − 4 a c for each equation and state the expected type of solutions.ī 2 − 4 a c = ( 4 ) 2 − 4 ( 1 ) ( 4 ) = 0. So, in that sense, the operation of multiplication undoes the operation of factoring.

#Solving a quadratic equation by factoring plus

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 a ⋅ b = 0, a ⋅ b = 0, then a = 0 a = 0 or b = 0, b = 0, where a and b 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 2 x 2 + 3 x − 1 = 0 2 x 2 + 3 x − 1 = 0 and x 2 − 4 = 0 x 2 − 4 = 0 are quadratic equations. Solving Quadratic Equations by FactoringĪn equation containing a second-degree polynomial is called a quadratic equation. If there is a limited amount of space and we desire the largest monitor possible, how do we decide which one to choose? In this section, we will learn how to solve problems such as this using four different methods. Proportionally, the monitors appear very similar. The computer monitor on the left in Figure 1 is a 23.6-inch model and the one on the right is a 27-inch model.