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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

3.7 解一元高次方程式 Solve Higher-order Equation in One Variable – 练习题
Solve the following equations:
解下列方程式:
1. x^3 - 12x + 16 = 0

2. x^3 - 2x^2 + 5x - 4 = 0

3. 2x^3 + 5x^2 + x - 2 = 0

4. 4x^4 - 4x^3 + 7x^2 + x - 2 = 0

5. 2x^5 - 5x^4 - 7x^3 + 4x^2 + 5x + 1 = 0

6. (x + 1)^3 - 4(x + 1)^2 - 9(x + 1) - 4 = 0

7. 3(x^2 + x)^2 - 7(x^2 + x) + 2 = 0

8. (x + 1)(x + 3)(x - 2)(x - 4) = 24

9. (x - 1)(x - 2)(x + 3)(x + 4) = 36

10. (x - 1)(x - 2)(2x + 1)(2x + 3) = 6

11. (x^2 - x - 6)(x^2 + 3x - 4) + 24 = 0

12. 2x^4 + x^3 - 11x^2 + x + 2 = 0

13. 4x^4 - 4x^3 - 7x^2 - 4x + 4 = 0

14. x^4 + 3x^3 - 8x^2 + 3x +1 = 0

15. 2x^5 - x^4 + 2x^3 + 2x^2 - x + 2 = 0

16. x^5 + x^4 - 3x^3 + 3x^2 - x- 1 = 0

答案 Answer :

(1) – 4, 2

(2) 1

(3) ½, –2 , –1

(4) –½, ½

(5) –1, –½, 1, \frac{3\pm\sqrt{13}}{2}

(6) –2, \frac{3\pm\sqrt{41}}{2}

(7) –2, 1, \frac{-3\pm\sqrt{21}}{6}

(8) 0, 1, \frac{1\pm\sqrt{57}}{2}

(9) –1, -1\pm\sqrt{13}

(10) 0, ½, \frac{1\pm\sqrt{57}}{4}

(11) -3, 2, \frac{-1\pm\sqrt{33}}{2}

(12) ½, 2

(13) ½, 2

(14) 1, \frac{1}{2}(-5 \pm \sqrt{21})

(15) –1

(16) 1, \frac{-3\pm\sqrt5}{2}