Factoring quadratic equation4/28/2024 ![]() This can be expressed as the solution set − 4 3, 3 2 . The solutions to the quadratic equation ( 2 □ − 3 ) ( 3 □ + 4 ) = 0 are □ = 3 2 and The second equation can be solved by subtracting 4 from each side and then dividing by 3: The first equation can be solved by adding 3 to each side and then dividing by 2: We therefore have two linear equations to solve. The only way the product of these two expressions can be 0 is if one of the factors individually is equal to 0. We are given that the product of the two linear expressions ( 2 □ − 3 )Īnd ( 3 □ + 4 ) is 0. This quadratic equation is already in a factored form. In our first example, we will demonstrate the process of solving a quadratic equation given its factored form.Įxample 1: Solving a Prefactored Equation It is important to remember that not every quadratic equation is factorable, so the methods we discuss here can only be applied to those that are. In some cases, the two solutions may coincide to give one repeated root, in which case we only give this value once as the solution. There are therefore two solutions, or roots, to the given quadratic equation: □ = − □ □ and □ = − □ □. So, to find all solutions to the given equation, we set each factor equal to 0, leading to two linear equations: The key to solving such an equation is to recognize that if the product of two (or more) factors is equal to 0, then at least one of the individual factors Suppose we have a quadratic equation in its factored form, The focus of this explainer is the application of these skills to solving quadratic equations. recognizing a quadratic as the difference of two squares,.recognizing a quadratic as a perfect square,. ![]() We should already be familiar with a number of methods for factoring quadratic expressions, including A quadratic equation is any equation that can be expressed in the form □ □ + □ □ + □ = 0 , where □, □,
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