Course Content
第四章:部分分式 Partial Fraction
0/1
第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
0/1
第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
0/2
高中一 | 高级数学
About Lesson

14.5 Higher Degree Inequalities in One Variable 一元高次不等式


Solve the inequalities
解下列不等式

(1)  (2 – x)(x + 1)(x – 3) \geq 0

(2) (2x – 3)(x – 1)(x + 1)(x + 3) < 0

(3)(a) (x – 3)(x – 1)^2(x + 1)^3(x + 3)^4 < 0

(3)(b) (x – 3)(x – 1)^2(x + 1)^3(x + 3)^4 > 0

(3)(c) (x – 3)(x – 1)^2(x + 1)^3(x + 3)^4 \leq 0

(3)(d) (x – 3)(x – 1)^2(x + 1)^3(x + 3)^4 \geq 0

(4) (x + 2)(x^2 – 2x – 4) > 0

(5) (1 – 2x)(x – 1)(x^2 + 2x + 3) < 0

(6) (x + 4)(x + 2)^2 > (3x – 2)(x + 2)^2

Answer :

(1) x \leq –1, 2 \leq x \leq 3

(2) –3 < x < –1, 1 < x < \frac{3}{2}

(3)(a) –1 < x < 1, 1 < x < 3

(3)(b) x < –3, –3 < x < –1, x > 3

(3)(c) –1 \leq x \leq 3, x = –3

(3)(d) x \leq –1, x \geq 3, x = 1

(4) -2 < x < 1 – \sqrt5, x > 1 + \sqrt5

(5) x < \frac{1}{2}, x > 1

(6) x < –2, –2 < x < 3

Exercise Files
No Attachment Found
No Attachment Found