mac1147_lecture5_2_b

# mac1147_lecture5_2_b - 5 L 5 Q u a d r a t i c E q u a t i...

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Unformatted text preview: 5 L 5 Q u a d r a t i c E q u a t i o n s a n d t h e Q u a d r a t i c F o r m u l a ; A p p l i c a t i o n s ; C o m p l e x N u m b e r s Q u a d r a t i c E q u a t i o n s A q u a d r a t i c e q u a t i o n i s a n e q u a t i o n o f t h e f o r m 2 a x b x c + + = w h e r e a , b , a n d c a r e r e a l n u m b e r s a n d a . S o l v i n g b y F a c t o r i n g Z e r o- P r o d u c t P r o p e r t y : I f a b = , t h e n E x a m p l e : S o l v e b y f a c t o r i n g . 2 1 9 x = − 2 4 1 2 9 x − + = 5 1 T h e S q u a r e R o o t s M e t h o d : T h e s o l u t i o n s e t t o 2 x p = ( ) p ≥ i s t h e s e t o f a l l s q u a r e r o o t s o f t h e n u m b e r p , t h a t i s x p = ± E x a m p l e . S o l v e u s i n g t h e S q u a r e R o o t s M e t h o d . 2 2 5 x = 2 ( 2 ) 3 x + = S o l v i n g Q u a d r a t i c E q u a t i o n s b y C o m p l e t i n g t h e S q u a r e : 2 , a x b x c a + + = ≠ 1 . M a k e s u r e t h a t 1 a = ; i f n o t , d i v i d e e a c h t e r m b y a . 2 . G e t t h e c o n s t a n t o n t h e r i g h t- h a n d s i d e o f t h e e q u a t i o n . 3 . T a k e 1 / 2 o f t h e c o e f f i c i e n t o f x , s q u a r e i t , a n d a d d t h i s n u m b e r t o b o t h s i d e s o f t h e e q u a t i o n . 4 . F a c t o r t h e l e f t- h a n d s i d e i n t o a p e r f e c t s q u a r e ....
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## This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture5_2_b - 5 L 5 Q u a d r a t i c E q u a t i...

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