Cardans_Method - Extracting Roots from Cubic Polynomials Cardans Method Consider any cubic polynomial in x a3x3 a2x2 a1x ao = 0 This polynomial has

# Cardans_Method - Extracting Roots from Cubic Polynomials...

• Notes
• 1

This preview shows page 1 out of 1 page.

Extracting Roots from Cubic Polynomials - Cardan’s Method Consider any cubic polynomial in x , a 3 x 3 + a 2 x 2 + a 1 x + a o = 0 This polynomial has three roots; one must be real and the other two may be real or imaginary. The three roots can be found analytically using Cardan’s Method, which is described below. To obtain the real roots to any cubic having real coefficients, first write your cubic in this form: x 3 + bx 2 + cx + d = 0 Then compute p = 2 b 3 " 9 bc #### You've reached the end of your free preview.

Want to read the whole page?

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 ( )...
View Full Document

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern  