Solving for X Intercepts: How to Find the Real Answers for x^3-3x^2+3

  • Thread starter Thread starter Whalstib
  • Start date Start date
Click For Summary

Homework Help Overview

The problem involves finding the x-intercepts of the cubic polynomial x^3 - 3x^2 + 3. The original poster expresses confusion over the mathematical determination of these intercepts, noting discrepancies between graphical observations and algebraic results.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the inapplicability of the quadratic formula due to the polynomial's degree. There are suggestions to consider polynomial long division and the Rational Roots Theorem, although some express skepticism about their effectiveness. Others propose numerical methods or graphing to estimate roots.

Discussion Status

The discussion is ongoing, with various methods being explored. Some participants are questioning the assumptions about the polynomial's roots and the applicability of certain algebraic techniques. There is no explicit consensus on a single approach, but several lines of reasoning are being examined.

Contextual Notes

Participants note that the problem may exceed the expected capabilities of a calculus 1 student, raising concerns about the alignment of the problem with the instructional material provided.

Whalstib
Messages
119
Reaction score
0

Homework Statement


Find x intercept of:

x^3-3 x^2+3


Homework Equations



I can clearly see three x intercepts on the graph but can not determine them mathematically. Quadratic formula and calculator give non real answer. Book says: ( -.879, 0) (1.347,0) (2.5232, 0)


The Attempt at a Solution



I am totally stuck as the quadratic gives a negative discriminant and a non real answer... yet there are indeed three intercepts.

What am I doing wrong?

Thanks,

Warren
 
Physics news on Phys.org
I don't think you could use the quad. formula here because it's not in the form of ax^2+bx+c. Did you go over division? I believe you have to use long division to find the zeroes.
 
stratusfactio said:
I don't think you could use the quad. formula here because it's not in the form of ax^2+bx+c.
I agree.
Well, I don't know about finding exact roots, but you can get a general idea of where the zeroes are by plugging in a few numbers. For example, with x=1 you get a positive answer, but with x=-1 you get a negative answer. So in between x=1 and x=-1 there is a root.
 
stratusfactio said:
I don't think you could use the quad. formula here because it's not in the form of ax^2+bx+c. Did you go over division? I believe you have to use long division to find the zeroes.

D'oh! Of course! Man, it is possible to study too long...! I'm still at a loss...

I'm not sure how to work the division...any hints?...

Thanks,

Warren
 
There's the Rational Roots Theorem, but it's not going to work in this case, because you can see that all three roots are irrational. There's the Cubic Formula, but it's very complicated to use. Outside of those two methods, you're not going to be able to solve this algebraically.
 
Durand Kerner method?
 
So...

Use the calculator and zero function to estimate is all that could possibly be expected from a calc 1 student right?
I got to say this is so typical of the Larson Calculus of a Single Variable book! Each chapter has problems that are near impossible to solve with the instruction given to that point.

When learning the product rule several problems were given that demanded quotient rule and the answer book gave the the answer as quotient rule form. unfortunately quotient rule isn't presented till the next section!

Thanks,

Warren
 
I have a friend who took college algebra for the extra A (he tested out of it) and he swears they had to solve cubic equations.

But... here you go.

cubic.gif
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
Replies
19
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
21
Views
4K