The Quadratic Formula

Algebra QUADRATIC EQUATIONS The Quadratic Formula Many quadratic equations cannot readily be solved by either of the two techniques already described (taking the square roots or factoring). For example, the quadratic equation x² - 6x + 4 = 0 is not a pure quadratic and, therefore, cannot be solved by taking the square roots. In addition, the left-hand side of the equation cannot readily be factored. The Quadratic Formula is a third technique for solving quadratic equations. It can be used to find the roots of any quadratic equation. (2-8) x b ± b² 4ac 2a Equation 2-8 is the Quadratic Formula. It states that the two roots of a quadratic equation written in general form, ax² + bx + c = 0, are equal to x = and b b² 4ac 2a x = . The Quadratic Formula should be committed to memory because it is b b² 4ac 2a such a useful tool for solving quadratic equations. There are three steps in solving a quadratic equation using the Quadratic Formula. Step 1. Write the equation in general form. Step 2. Substitute the values for a, b, and c into the Quadratic Formula and solve for x. Step 3. Check the roots in the original equation. Rev. 0 Page 25 MA-02