Step 5: Solve using the square root property. ax 3 4 b 2 17 16 x 3 4 B 17 16 x 3 4 117 4 116 4 x 3 4 117 4 Subtract 3 4 . x 3 117 4 Same denominators, combine numerators. ax b 2a b 2 x b 2a x b 2a x b 2a x b 2b2 4ac The result on the right is called the quadratic formula. b2 4ac 4a2 B b2 4ac 4a2 2b2 4ac 2a 24a2 2a 2b2 4ac 2a Subtract b 2a . 2a Same denominators, combine numerators. Definition The Quadratic Formula The solutions of any quadratic equation of the form ax2 bx c 0 (a 0) are x b 2b2 4ac 2a This is called the quadratic formula. Note 1) The equation to be solved must be written in the form ax2 bx c 0 so that a, b, and c can be identified correctly. 2) x b 2b2 4ac 2a represents the two solutions x b 2b2 4ac 2a and x b 2b2 4ac 2a . 3) Notice that the fraction bar continues under b and does not end at the radical. x b 2b2 4ac 2a x b 2b2 4ac 2a Correct Incorrect 4) Using the when deriving the quadratic formula allows us to say that 24a2 2a. 5) The quadratic formula is a very important result and is one that is used often. It should be memorized! You can use the quadratic formula to solve any quadratic equation as long as it is in the form ax2 bx c 0. 622 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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