![]() Let us solve an example to understand the factoring quadratic equations by taking the GCD out.Ĭonsider this quadratic equation: 3x 2 + 6x = 0 Using Algebraic Identities (Completing the Squares)įactoring Quadratics by Taking Out The GCDįactoring quadratics can be done by finding the common numeric factor and the algebraic factors shared by the terms in the quadratic equation and then take them out.There are different methods that can be used for factoring quadratic equations. Thus the equation has 2 factors (x+3) and (x-3)įactoring quadratics gives us the roots of the quadratic equation. Verify by substituting the roots in the given equation and check if the value equals 0. Thus the equation has 2 factors (x + 3) and (x + 2)ģ and -3 are the two roots of the equation. Consider the quadratic equation x 2 + 5x + 6 = 0 Let us go through some examples of factoring quadratics:ġ. Hence, factoring quadratics is a method of expressing the quadratic equations as a product of its linear factors, that is, f(x) = (x - \(\alpha\))(x - \(\beta\)). Thus, (x - \(\beta\)) should be a factor of f(x). Similarly, if x = \(\beta\) is the second root of f(x) = 0, then x = \(\beta\) is a zero of f(x). Thus, (x - \(\alpha\)) should be a factor of f(x). This means that x = \(\alpha\) is a zero of the quadratic expression f(x). Suppose that x = \(\alpha\) is one root of this equation. Consider a quadratic equation f(x) = 0, where f(x) is a polynomial of degree 2. They are the zeros of the quadratic equation. Every quadratic equation has two roots, say \(\alpha\) and \(\beta\). The factor theorem relates the linear factors and the zeros of any polynomial. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc. This method is also is called the method of factorization of quadratic equations. Any other quadratic equation is best solved by using the Quadratic Formula.Factoring quadratics is a method of expressing the quadratic equation ax 2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax 2 + bx + c = 0. If the equation fits the form ax 2 = k or a( x − h) 2 = k, it can easily be solved by using the Square Root Property. If the quadratic factors easily, this method is very quick. How to identify the most appropriate method to solve a quadratic equation. ![]() if b 2 − 4 ac if b 2 − 4 ac = 0, the equation has 1 real solution.If b 2 − 4 ac > 0, the equation has 2 real solutions.For a quadratic equation of the form ax 2 + bx + c = 0,.Using the Discriminant, b 2 − 4 ac, to Determine the Number and Type of Solutions of a Quadratic Equation.Then substitute in the values of a, b, c. Write the quadratic equation in standard form, ax 2 + bx + c = 0.How to solve a quadratic equation using the Quadratic Formula.We start with the standard form of a quadratic equation and solve it for x by completing the square. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. ![]() Solve Quadratic Equations Using the Quadratic Formula
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |