promotion image of download ymail app
Promoted

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

3 Answers

Relevance
  • sepia
    Lv 7
    2 months ago

    x^4 - x^3 - 12x^2 - 3x + 1 = 0

    Solutions:

    x ≈ -2.8262

    x ≈ -0.45756

    x ≈ 0.18885

    x ≈ 4.0949

    • Commenter avatarLogin to reply the answers
  • 2 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

    • Commenter avatarLogin to reply the answers
  • david
    Lv 7
    2 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?

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.