107. DISCUSS PROVE: The Depressed Cubic The most gen- eral cubic (third-degree) equation with rational coefficients can be written as x* + ax? + bx + c = 0 (a) Prove that if we replace x by X – a/3 and simplify, we end up with an equation that doesn't have an X term., that is, an equation of the form X + pX + q = 0 This is called a depressed cubic, because we have "depressed" the quadratic term. (b) Use the procedure described in part (a) to depress the equation x + 6x² + 9x + 4 = 0.

107. DISCUSS PROVE: The Depressed Cubic The most gen- eral cubic (third-degree) equation with rational coefficients can be written as x* + ax? + bx + c = 0 (a) Prove that if we replace x by X – a/3 and simplify, we end up with an equation that doesn't have an X term., that is, an equation of the form X + pX + q = 0 This is called a depressed cubic, because we have "depressed" the quadratic term. (b) Use the procedure described in part (a) to depress the equation x + 6x² + 9x + 4 = 0.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

107. DISCUSS PROVE: The Depressed Cubic The most gen-
eral cubic (third-degree) equation with rational coefficients
can be written as
x* + ax? + bx + c = 0
(a) Prove that if we replace x by X – a/3 and simplify, we
end up with an equation that doesn't have an X term.,
that is, an equation of the form
X + pX + q = 0
This is called a depressed cubic, because we have
"depressed" the quadratic term.
(b) Use the procedure described in part (a) to depress the
equation x + 6x² + 9x + 4 = 0.

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