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How to solve this? Please help!

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- Thread starter SELFMADE
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In summary, the problem is that x-1 does not meet the requirements for a rational root. There are only two possibilities for x-1, and neither of them work. One is x-1=2 and the other is x-1=-1. But neither of those work because x-1+1 and x-1-1 are not equal. So this equation has no rational roots.f

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How to solve this? Please help!

- #2

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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

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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

this is what i have so far:

x^2 - x

_______x to eliminate the power

x - 1

_______x

i'm pretty much stuck there, any help?

p.s. underscore is just to put the X where i want it

- #5

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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

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Please do not "hijack" other people's threads for a new problem. And, I can see no similarity, except that they both involve polynomials.

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

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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