Roots of a Cubic Function: Solving for x

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In summary, the conversation is about a person struggling to solve the equation x3-8x+5=0 and seeking help. They initially write the equation incorrectly and are reminded that an equation must have an = in it. They then mention their attempts at factoring and using the equation x(x-√8)(x+√8)+5=0. Other users question if the equation is correct and suggest using a graphing or approximation technique due to the lack of rational roots. The person confirms that the original equation is correct and is asked about their course and methods they have studied. No solution is provided.
  • #1
trivk96
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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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  • #2
There's no question here.

What are you trying to do / get to ??
 
  • #3
Sorry... solve for x
 
  • #4
You can't solve for x - you don't have an equation.
 
  • #5
x3-8x+5 is the equation
 
  • #6
trivk96 said:
x3-8x+5 is the equation
This is NOT an equation. An equation ALWAYS has an = in it.
 
  • #7
Mark44 said:
This is NOT an equation. An equation ALWAYS has an = in it.
Sorry...x3-8x+5=0
 
  • #8
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:
  • #9
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?
 

FAQ: Roots of a Cubic Function: Solving for x

What is a cubic function?

A cubic function is a type of polynomial function that has a degree of 3, meaning it contains variables raised to the third power, such as x³. It can be written in the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants.

How do you solve for x in a cubic function?

To solve for x in a cubic function, you must first set the function equal to zero. Then, you can use various methods such as the rational root theorem, synthetic division, or the cubic formula to find the roots or solutions for x.

What is the rational root theorem?

The rational root theorem is a method for finding the rational roots or solutions of a polynomial function, including cubic functions. It states that if a polynomial has rational roots, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

How do you use synthetic division to solve for x in a cubic function?

Synthetic division is a shortcut method for dividing polynomials. To use it to solve for x in a cubic function, you must first set the function equal to zero and then use the rational root theorem to find a possible rational root. This root can then be used in the synthetic division process to find the remaining roots or solutions for x.

What is the cubic formula?

The cubic formula is a formula used to find the roots or solutions of a cubic function. It is a complex formula that involves taking the cube root of a number and can be used when the rational root theorem and synthetic division methods are not applicable. However, it is often not used due to its complexity and the availability of more efficient methods.

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