# find all distinct actual rational solutions of a polynomial equations, x^4-X^3-12x^3-3x+1=0?

### 3 Answers

- sepiaLv 72 months ago
x^4 - x^3 - 12x^2 - 3x + 1 = 0

Solutions:

x ≈ -2.8262

x ≈ -0.45756

x ≈ 0.18885

x ≈ 4.0949

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- cryptogramcornerLv 62 months ago
Lets assume that you meant -12x^2. Consider what you would have if you factored this equation: it would be (x - r1) (x - r2) (x - r3) (x - r4). If you think about how this would be multiplied out, all the x's will combine to get the x^4 term, and all the roots will combine to get the constant term. r1 x r2 x r3 x r4 = 1. If any of the roots are rational they have to be +/- factors of 1. The only possible rational roots are therefore 1 and -1. Try plugging 1 or -1 into the polynomial, and neither one gets you 0, so there are no rational solutions to this equation

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- davidLv 72 months ago
is there a typing mistake?

x^4-X^3-12x^3-3x+1=0 two x^3 terms

x^4-x^3-12x^2-3x+1=0 <<< maybe this?

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