Roots of a Cubic Function: Solving for x

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The discussion revolves around solving the cubic equation x³ - 8x + 5 = 0. Initially, the user mistakenly presented the polynomial without an equation, leading to confusion. Once clarified, it was noted that the polynomial does not have rational roots, suggesting the need for graphing or approximation methods for solutions. Participants questioned the user's understanding of cubic equations and whether they had been taught relevant solving techniques. The conversation emphasizes the importance of correctly identifying and presenting mathematical problems for effective assistance.
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Homework Statement


x3-8x+5


Homework Equations





The Attempt at a Solution


I am stuck here. I tried factoring.
 
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There's no question here.

What are you trying to do / get to ??
 
Sorry... solve for x
 
You can't solve for x - you don't have an equation.
 
x3-8x+5 is the equation
 
trivk96 said:
x3-8x+5 is the equation
This is NOT an equation. An equation ALWAYS has an = in it.
 
Mark44 said:
This is NOT an equation. An equation ALWAYS has an = in it.
Sorry...x3-8x+5=0
 
OK, finally an equation.

Your polynomial doesn't have any nice (i.e., rational) roots, so short of using a very complicated formula from about the 16th century, it looks to me like you need to get the root or roots by graphing the function or using some approximation technique.

What is the complete problem description?
 
Last edited:
Sorry about my terrible earlier posts...

The problem asks me to solve x3-8x+5=0 algebraically

heres what i have gotten to so far. Not sure if this will help me:

i made the original equation into x(x-√8)(x+√8)+5=0
 
Last edited:
  • #10
trivk96 said:
Sorry about my terrible earlier posts...

The problem asks me to solve x3-8x+5=0 algebraically

Did you copy the problem correctly? Are you sure it's not x2-8x+5=0? Otherwise, your problem has no answer (other than using the cubic formula).
 
  • #11
Are you absolutely sure this is the equation you're supposed to solve?
x3-8x+5=0

Has your teacher shown you a technique for solving cubic equations? If not, you can't be expected to solve this one.
 
  • #12
x3-8x+5=-2

is nicer.
 
  • #13
trivk96 said:

Homework Statement


x3-8x+5


Homework Equations





The Attempt at a Solution


I am stuck here. I tried factoring.

supposed to be, x3-8x+5=0.

What course are you in? What methods and techniques have you studied so far? Do you know how many and what kind of roots this equation should have?
 

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