Factoring Quadratic Equations

Algebra QUADRATIC EQUATIONS Step 4. Check the roots. 2x² 3 4x x² 1 2^� � � � � � 2 3 2 3 4^� � � � � � 2 3 � � � � � � 2 3 2 1 2^� � � � � � 4 9 3 8 3 4 9 1 8 9 27 9 24 9 4 9 9 9 19 9 19 9 2x² 3 4x x² 1 2(2)² 3 4(2) (2)² 1 2(4) 3 8 4 1 8 3 5 5 5 Thus, the roots check. Quadratic equations in which the numerical constant c is zero can always be solved by factoring. One of the two roots is zero. For example, the quadratic equation 2x² + 3x = 0 can be solved by factoring. The factors are (x) and (2x + 3). Thus, the roots are x = 0 and x = - . If a 3 2 quadratic equation in which the numerical constant c is zero is written in general form, a general expression can be written for its roots. The general form of a quadratic equation in which the numerical constant c is zero is the following: ax² + bx = 0 (2-4) The left-hand side of this equation can be factored by removing an x from each term. x(ax + b) = 0 (2-5) Rev. 0 Page 23 MA-02