Help solving a complex x-cubed problem

A

alexe

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Apr 2, 2009
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How would one solve this problem:

x^3 - 15(x^2) + 3x - 5 = 0

Thanks.
 
A good way usually is to try to factorise it... however, this ends up not working.

What kind of answer do you want? An exact algebraic answer? An approximate answer to a certain number of decimal places?

Is this problem part of a course? If so, have you been taught certain methods for solving equations? Or cubics? Are you certain that you typed the question in correctly?

Did you come across this problem when investigating something else? If so, you can use any method you like... I'd recommend Newton's method or the bisection method - or for something very approximate, the "graph it and look" method....
 
Most cubic polynomials are not easily factorable.
This one might be simplified using Synthetic Division to reduce to a quadratic, which is much easier to factor.
 
BTW, this cubic is quite amenable to Synthetic Division.
The only possible rational zeros are ±1 and ±5. It won't take long to substitute each of those into the equation.
 
fasteddie65 said:
BTW, this cubic is quite amenable to Synthetic Division. ? It is not - because it does not have a rational root.

The only possible rational zeros are ±1 and ±5. It won't take long to substitute each of those into the equation. ... and none of those work ...
Click to expand...

This one has one real root at 14 - 15 and others are complex.

Best way to approximate the root is to use the "trace" function of the graphical calculator (other than using good ole Newton).
 
DrMike said:
A good way usually is to try to factorise it... however, this ends up not working.

What kind of answer do you want? An exact algebraic answer? An approximate answer to a certain number of decimal places?

Is this problem part of a course? If so, have you been taught certain methods for solving equations? Or cubics? Are you certain that you typed the question in correctly?

Did you come across this problem when investigating something else? If so, you can use any method you like... I'd recommend Newton's method or the bisection method - or for something very approximate, the "graph it and look" method....
Click to expand...

This is equation came up as a 2nd derivative of a calculus problem I was solving. I am expected to figure out the points of inflection. I have typed it in correctly and synthetic division, factoring don't work. I will research Newton's method and bisection method (links would be appreciated) as I have never heard of them before, or I forgot about them. Any further suggestions will be appreciated.

Thanks all.
 
alexe said:
DrMike said:
A good way usually is to try to factorise it... however, this ends up not working.

What kind of answer do you want? An exact algebraic answer? An approximate answer to a certain number of decimal places?

Is this problem part of a course? If so, have you been taught certain methods for solving equations? Or cubics? Are you certain that you typed the question in correctly?

Did you come across this problem when investigating something else? If so, you can use any method you like... I'd recommend Newton's method or the bisection method - or for something very approximate, the "graph it and look" method....
Click to expand...

This is equation came up as a 2nd derivative of a calculus problem I was solving. I am expected to figure out the points of inflection. I have typed it in correctly and synthetic division, factoring don't work. I will research Newton's method and bisection method (links would be appreciated) as I have never heard of them before, or I forgot about them. Any further suggestions will be appreciated.

Thanks all.
Click to expand...

You are right that factoring etc won't work on this cubic, because the cubic has no rational roots.

The only other suggestion I would make is... check your differentiation (or ask one of us to).
 
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