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Unformatted text preview: 9 bc + 27 d 54 and q = b 2 " 3 c 9 If ( p 2 q 3 ) > 0, then the cubic has only one real root, x = " sgn( p ) r 2 + q r # $ % & ( " b 3 where sgn( p ) = p / p  and r = p 2 " q 3 + p ( ) 1/ 3 But if ( p 2 q 3 ) 0, then the cubic has three real roots, x 1 = (2 q )cos( /3) ( b /3) x 2 = (2 q )cos[( + 2 )/3] ( b /3) x 3 = (2 q )cos[( + 4 )/3] ( b /3) where " = cos # 1 p q 3 ( )...
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This note was uploaded on 09/20/2008 for the course CHEM 202 taught by Professor John during the Spring '08 term at UVA.
 Spring '08
 John

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