§ 3. Ìíîãî÷ëåíû íàä ÷èñëîâûìè ïîëÿìè

                 ¹ 34. Ïîëüçóÿñü êðèòåðèåì Ýéçåíøòåéíà,äîêàæèòå
íåïðèâîäèìîñòü íàä ïîëåì ðàöèîíàëüíûõ ÷èñåë Q ìíîãî÷ëåíîâ.

34.01.

f(x) = 2x5 + 21x4 – 15õ3 + 24;

34.02.

f(x) = 3x100 – 13x  + 52;

34.03.

f(x) = x4 – 2õ + 3;

34.04.

f(x) = 4x7 – 14x 5 – 21õ3 + 28õ2 – 49õ + 15;

34.05.

f(x) = 2x4 + 9x3 + 20õ2 + 15õ + 32;

34.06.

f(x) = 4x7 – 14x 5 – 21õ3 + 28õ2 – 49õ + 15;

34.07.                

f(x) = 2x5 + 6x4 – 9õ2 + 12;

34.08.

f(x) = 3x4 – 22x3 + 60õ2 – 76õ + 28;

34.09.                

f(x) = x4 – x3 + 2õ + 1;

34.10.

f(x) = x4 – 8x3 + 12õ2 – 6õ + 2;

34.11.                

f(x) = x5 – 12x3 + 36õ – 12;

34.12.

f(x) = 3x4 – 15x3 + 10õ2 – 20õ + 35;

34.13.                

f(x) = x7 – 7x + 13;

34.14.

f(x) = 2x5 + 14x3 – 35õ2 – 56õ + 63;

34.15.                

f(x) = x3 + 3x2 + 3õ + 10;

34.16.

f(x) = x5 + 5x4 + 5õ + 16;

34.17.                

f(x) = x5 – 5x + 9;

34.18.

f(x) = x7 + 7x6 + 7õ + 22;

34.19.

f(x) = 6x3 – 30x + 15;

34.20.

f(x) = 5x5 + 6x4 – 144õ3 + 18õ2 – 42õ + 12;

34.21.

f(x) = 9x5 + 63x3 – 14õ2 + 28;

34.22.

f(x) = x4 + 12õ3 + 21õ2 – 3õ + 33;

34.23.                

f(x) = x4 + 3x + 11
(Óêàçàíèå. Ââåñòè õ = ó + 1);

34.24.

f(x) = 12x5 + 11x3 + 33õ – 44;

34.25.

f(x) = x5 + 44x4 – 22õ3 + 121õ2 – 33;

34.26.

f(x) = 2x5 + 14x4 – 21õ3 + 63õ2 – 7õ + 35;

34.27.

f(x) = 2x5 – 14x4 – 42õ2 + 14õ + 21;

34.28.

f(x) = x5 – 6x4 + 9õ3 – 12õ + 15;

34.29.

f(x) = 4x4 – 26õ3 + 39õ2 + 52õ – 33;

34.30.

f(x) = x5 – 2x4 + 4õ3 + 36õ2 – 42õ + 6;

34.31.

f(x) = 2x5 – 6x4 + 9õ3 – 27õ2 – 3õ – 12;

34.32.

f(x) = 2x5 – 10x4 + 125õ3 – 25õ2 – 15õ – 15;

34.33.

f(x) = 4x4 – 12x3 +  27õ2 – 15õ + 6;

34.34.

f(x) = 3x6 – 14x5 – 21õ3 + 42õ2 – 14õ – 28;

34.35.

f(x) = 9x5 – 28õ4 + 56õ3 – 56õ2 + 14x – 21;

34.36.

f(x) = 5x6 – 26x5 + 39õ3 – 52õ2 – 26õ – 65;

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