Theory of cubic equation question

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    Cubic Theory
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The discussion revolves around finding the cubic equation whose roots are the squares of the roots of the original equation x^3 - 4x^2 + x - 1 = 0. Participants clarify that an equation must include an equal sign and engage in algebraic manipulations to derive the new polynomial. The correct approach involves expressing the roots of the original polynomial as a, b, and c, then forming a new polynomial with roots a^2, b^2, and c^2. Several participants emphasize the importance of careful algebraic steps and the correct application of symmetric polynomials. Ultimately, the final equation derived is x^3 - 14x^2 - 7x - 1 = 0.
  • #31
lionely said:
sighh sigh sighj sigh sigh sigh sigh why didn't i see that ...

(1+4x)^2 = 1 + 8x + 16x^2...

VERY GOOD. Finally. OK, now just simplify and group the terms.

Remember to expand the LHS correctly too. :smile:

BTW, if you're working in the variable 'y', you should use that throughout, otherwise it's confusing (and actually wrong).
 
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  • #32
it is x3 -14x2+x-1
 
  • #33
lionely said:
it is x3 -14x2+x-1

Not quite. Every coefficient is right except the one for the x term. You must have made a mistake, show your exact work.

A bit of a cheat, but you can test your answer here: http://www.gyplan.com/eqcubic_en.html

And, not to belabour the point, what you wrote is still not an equation! You MUST put the '=0'.
 
  • #34
lol... x^3 -14x^2-7x-1
 
  • #35
lionely said:
lol... x^3 -14x^2-7x-1

Still not an equation. Just an expression. But all the coefficients are right.
 
  • #36
looooooool OKAY HERE IT IS x^3 -14x^2-7x-1 = 0!
 
  • #37
lionely said:
looooooool OKAY HERE IT IS x^3 -14x^2-7x-1 = 0!

GREAT!:biggrin:
 

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