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Lv 7
? asked in Science & MathematicsMathematics · 3 years ago

Please help. 3x^3-x^2-5x+7=0(mod 11), find all possible x.?

1 Answer

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  • Puzzling
    Lv 7
    3 years ago

    Try values of x from 0 to 10:

    f(x) = 3x^3 - x^2 - 5x + 7

    f(0) = 0 - 0 - 0 + 7 ≡ 7 ≠ 0 (mod 11)

    f(1) = 3 - 1 - 5 + 7 ≡ 4 ≠ 0 (mod 11)

    ...

    f(9) = 3*729 - 81 - 45 + 7

    f(9) ≡ -2 - 4 - 1 + 7 = 0 (mod 11)

    Answer:

    x = 11n + 9, where n is an integer

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