How to solve x^3-x-1=0

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How to solve this? Please help!
 

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  • #2
symbolipoint
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If you can divide the polynomial expression by a linear binomial, then you can determine what value of x of each binomial will make the binomial equal to zero. Try first divisors x+1, and x-1.
 
  • #3
HallsofIvy
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By the "rational root theorem", which says that if m/n (m and n integers) is a rational root of [itex]a_nx^n+ a_{n-1}x^{n-1}+\cdot\cdot\cdot+ a_1x+ a_0[/itex] then n must divide the "leading coefficient", [itex]a_n[/itex], and m must divide the "constant term", a_0. That tells us that the only possible rational roots for this equation are the intgers 1 and -1. Unfortunately, trying them [itex]1^3- 1- 1= -1[/itex] and [itex](-1)^3- (-1)-1= -1[/itex]. Since neither of those is equal neither 1 nor -1 is a root and so this equation has no rational roots.

But if x= 2, [itex]2^3- 2- 1= 5[/itex] so there is clearly a root between 1 and 2. The only thing I could suggest is Cardano's "cubic formula": http://www.sosmath.com/algebra/factor/fac11/fac11.html.
 
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  • #4
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i have a similar problem

x^2 -x -20 < 0

this is what i have so far:

x^2 - x < 20

x^2 - x < 20
_______x to eliminate the power

x - 1 < 20
_______x


i'm pretty much stuck there, any help?
p.s. underscore is just to put the X where i want it
 
  • #5
rock.freak667
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What exactly are you to do with that inequality? Find the range of values for x?



x - 1 < 20
_______x

I think at one point you divided by x to get this, but you can't just divide by x in an inequality, as the sign of x can change the inequality.

But if you want to get [itex]x^2-x-20[/itex] to have x to a single power then try completing the square.
 
  • #6
HallsofIvy
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i have a similar problem

x^2 -x -20 < 0

this is what i have so far:

x^2 - x < 20

x^2 - x < 20
_______x to eliminate the power

x - 1 < 20
_______x


i'm pretty much stuck there, any help?
p.s. underscore is just to put the X where i want it
Please do not "hijack" other people's threads for a new problem. And, I can see no similarity, except that they both involve polynomials.

I recommend you factor [itex]x^2- x- 20[/itex] which can be done relatively easily. Use the fact that the product of two numbers is negative if and only if one is positive and the other negative.
 
  • #7
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My bad, thanks for the help though.
 

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