Zadachi

§ 3. Многочлены над числовыми полями

№ 29. Дан многочлен f(x) сдействительными коэффициентами.
Зная, что a - корень многочлена f(x), найдите остальные его корни.
29.01.
f(x) = x⁴– x³ – 2х² + 6х – 4,a = 1 – i;
29.02.
f(x) = x³ – 4х² + 9х – 10,a = 1 – 2i;
29.03.
f(x) = x⁴+x³ +13х² + 47х + 34,a = 1 + 4i;
29.04.
f(x) = x³ – 2х² – 3х + 10,a = 2 + i;
29.05.
f(x) = x⁴– 2x³ – 11х² + 42х – 40,a = 2 – i;
29.06.
f(x) = x³ – 4х² + 6х – 4,a = 1 – i;
29.07.
f(x) = x⁴– 6x³ + 13х² – 14х + 6,a = 1 + i;
29.08.
f(x) = x³ – 7х² + 17х – 15,a = 2 – i;
29.09.
f(x) = x⁴– 7x³ + 19х² – 23х + 10,a = 2 – i;
29.10.
f f(x) = х⁴ – 3x³ + 10х² – 6х – 20,a = 1 + 3i;
29.11.
f(x) = x³ – 7х² + 17х – 15,a = 2 – i;
29.12.
f(x) = x³ – 7х² + 16х – 10,a = 3 + i;
29.13.
f(x) = x⁴– 13x³ + 58х² – 98х + 52,a = 5 – i;
29.14.
f(x) = x³ – 8х² + 22х – 20,a = 3 + i;
29.15.
f(x) = x³ – 16х² + 53х – 60,a = 2 – i;
29.16.
f(x) = x³ – 3х² + 7х – 5,a = 1 + 2i;
29.17.
f(x) = x⁴– 2x³ – 11х² + 42х – 40,a = 2 – i;
29.18.
f(x) = х⁴ – 9x³ + 22х² + 28х – 120,a = 4 + 2i;
29.19.
f(x) = x⁴– 6x³ + 13х² – 14х + 6,a = 1 + i;
29.20.
f(x) = x⁴– 3x³ + 3х² + 37х – 78,a = 2 – 3i;
29.21.
f(x) = x⁴– 11x³ + 9х² + 245х – 100,a = 4 + 3i;
29.22.
f(x) = x⁴– 7x³ + 7х² + 59х – 156,a = 3 + 2i;
29.23.
f(x) = x⁴– 8x³ + 20х² – 45х + 75,a = 1 + 2i;
29.24.
f(x) = x⁴– 7x³ + 7х² – 364,a = 2 – 3i;
29.25.
f(x) = x⁴– 5x³ + 5х² + 35х – 156,a = 2 + 3i;
29.26.
f(x) = x⁴– 6x³ – 12х² + 150х – 325,a = 3 + 2i;
29.27.
f(x) = x⁴– 8x³ + 20х² – 40х + 75,a = 1 – 2i;
29.28.
f(x) = x⁴– 6x³ – 3х² + 86х – 208,a = 3 + 2i;
29.29.
f(x) = x³ – 7х² + 17х – 15,a = 2 – i;
29.30.
f(x) = x⁴+ 3x³ – 21х² – 3х + 260,a = 3 – 2i;
29.31.
f(x) = x⁴+ 15x³ + 31х² – 45х + 22,a = 3 – 2i;
29.32.
f(x) = x⁴– 4x³ – 2х² + 44х – 39,a = 3 – 2i;
29.33.
f(x) = x⁴– 7x³ – 3х² + 73х – 364,a = 2 + 3i;
29.34.
f(x) = x⁴– 3x³ + 17х² – 13х – 34,a = 1 – 4i;
29.35.
f(x) = x⁴– 9x³ + 33х² – 51х + 26,a = 2 + 3i;
29.36.
f(x) = x⁴– 17x³ + 109х² – 323х + 390,a = 3 – 2i.

\.Пример.\