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( θ /3) – ( b /3) x 2 = (2 q )cos[( θ + 2 π )/3] – ( b /3) x 3 = (2 q )cos[( θ + 4 π )/3] – ( b /3) where " = cos # 1 p q 3 ( )...
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 Spring '08
 John
 Fundamental Theorem Of Algebra, Polynomials, Quadratic equation, Complex number, cubic polynomial, Cubic Polynomials

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