§ 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;