Unformatted text preview: = 0 can be solved as follows. First, divide by a to obtain an equation of the form x 3 + Bx 2 + Cx + D = 0. Next, make the substitution x = zB 3 . This will convert the equation to the form z 3 + pz + q = 0. Thirdly, make the substitution z = wp 3 w . This will convert the equation to the form w 3 + r w3 + q = 0. Finally, multiply through by w 3 to obtain w 6 + q w 3 + r = 0, which we can solve for w 3 using the Quadratic Formula. (You may ﬁnd section 9.6 useful). (a) Solve x 33 x + 1 = 0 for x ∈ R . (b) Solve x 3 + 3 x 23 x7 = 0 for x ∈ R ....
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This note was uploaded on 07/25/2011 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS
 Algebra, Complex Numbers

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