7/9/2013 Quadratic Equations 21 Quadratic Formula Examples Example 1 Solve: 7x 2 + 9x + 29 = 27 x =  ± –9–9 9 2 – 4 7 2 (( ) ) 2 7 ( ) = ± –9–9  81 – 56 14 = ± –9–9  2525 = ± –9–9 5 Question:Are there always two solutions .
{"Image DocumentName": "Quadratic Formula Examples", "Image ImageDescription": "Solving Quadratic Equations. Example 1. Solve: 7x2 + 9x + 29 = 27. (continued) x. = \uf0d6 \u20139. 92 \u2013 ( ) 2 7. = \u20139. \uf0d6 81 \u2013 = \u20139. \uf0d6 = \u2013 = \u2013 The Quadratic Formula: Example 1. Here we apply the quadratic formula to solve a quadratic equation. Note that the formula applies to the standard form of the quadratic equation, that is. ax2 + bx + c = 0. with the coefficients appearing in the formula. If the equation is not already in standard form, then it must be rewritten in that form to apply the formula. The values of a, b, and c are shown and substituted directly in the formula. The calculations from that point are straight forward. Choosing first the negative root and then the positive root we arrive at the two solutions shown. As long as the radicand (the quantity under the radical) is non-zero we will always have two solutions. However, if the radicand is zero, then we get only one solution (we will find that it is sometimes thought of as two identical solutions, i.e. a repeated root). \u2013 {\u20131, } \u2013 Solution set: Question: Are there always two solutions ? 7/9/2013. Quadratic Equations. Quadratic Equations. 7/9/2013.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}