what are the four methods for solving quadratic equations To solve quadratic equations start by combining all of the like terms and moving them to one side of the equation Then factor the expression and set each set of parentheses equal to 0 as separate equations Finally solve each equation separately to find the 2 possible values for x
A quadratic equation can be solved to obtain two values of x or the two roots of the equation There are four different methods to find the roots of the quadratic equation The four methods of solving the quadratic equations are as follows Factorizing of Quadratic Equation Using quadratic formula which we have seen already Methods for Solving Quadratic Equations Factoring Square Root Property Completing the Square Quadratic Formula Given that we have four methods to use to solve a quadratic equation how do you decide which one to use Factoring is often the quickest method and so we try it first
what are the four methods for solving quadratic equations
what are the four methods for solving quadratic equations
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1 Factorization method 2 Completing square method 3 Formula method 4 Graphical Method Solving Quadratic Equation by Factorization Method If we can factorize a x 2 b x c a 0 into a product of two linear factors then the roots of the quadratic equation a x 2 b x c 0 can be found by equating each factor to zero How to Solve Quadratic Equations There are basically four methods of solving quadratic equations They are Factoring Completing the square Using Quadratic Formula Taking the square root Factoring of Quadratics Begin with a equation of the form ax bx c 0 Ensure that it is set to adequate zero
Below are the 4 methods to solve quadratic equations Click on any link to learn more about a method The Quadratic Formula Factoring Completing the Square Factor by Grouping Examples of quadratic equations y 5x2 2x 5 y 11x2 22 y x2 4x 5 y x2 5 y 5 x 2 2 x 5 y 11 x 2 22 y x 2 4 x 5 y x 2 5 Develop a general strategy for solving quadratic equations Solve applications involving quadratic equations Discriminant If given a quadratic equation in standard form ax2 bx c 0 where a b and c are real numbers and a 0 then the solutions can be calculated using the quadratic formula
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1 FACTORING Set the equation equal to zero If the quadratic side is factorable factor then set each factor equal to zero Example x 2 5 x 6 Move all terms to one side Factor Set each factor to zero and solve x 2 5 x 6 0 x 3 x 2 0 3 0 x 2 0 3 x 2 2 PRINCIPLE OF SQUARE ROOTS Learning Objectives By the end of this section you will be able to Solve quadratic equations using the quadratic formula Use the discriminant to predict the number of solutions of a quadratic equation Identify the most appropriate method to use to solve a quadratic equation
Method 1 Solving the Quadratic Equation by Completing the Square Quadratic equations can be expressed as the square of linear equations so we can solve them simply by taking the square roots when taking the square roots we should aware of taking all possible square roots Positive and negative There are three basic methods for solving quadratic equations factoring using the quadratic formula and completing the square Factoring To solve a quadratic equation by factoring Put all terms on one side of the equal sign leaving zero on the other side Factor Set each factor equal to zero Solve each of these equations
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