Higher degree equations and inequalities

9000019807

Level:

Assuming

x \in R

, find the solution set of the following equation.

(3 x + 2) (x \sqrt{2} + 1) (x^{2} + 1) = 0

{- \frac{\sqrt{2}}{2}; - \frac{2}{3}}

{- \frac{2}{3}; \frac{1}{\sqrt{2}}}

{\frac{2}{3}; \frac{1}{\sqrt{2}}}

{- 1; - \frac{\sqrt{2}}{2}; - \frac{2}{3}}

9000025805

Level:

In the following list identify a true statement on the function

f

f (x) = (x + 1) (x + 2) (x - 3)

f (x) < 0 ⟺ x \in (- \infty; - 2) \cup (- 1; 3)

f (x) < 0 ⟺ x \in (- \infty; - \frac{3}{2}) \cup (1; 3)

f (x) < 0 ⟺ x \in (- \infty; - \frac{3}{2}) \cup (3; \infty)

f (x) < 0 ⟺ x \in (- \frac{3}{2}; - 1) \cup (3; \infty)

9000028306

Level:

Find the sum of all real solutions of the following equation.

(3 - x) (x^{2} - 4) = 0

3

0

2

5

1003029002

Level:

Find the solution set of the inequality.

(x^{2} - 1) (x^{2} - 3) > 0

(- \infty; - \sqrt{3}) \cup (- 1; 1) \cup (\sqrt{3}; \infty)

(- \sqrt{3}; - 1) \cup (1; \sqrt{3})

(- \infty; - \sqrt{3}) \cup (1; \sqrt{3}) \cup (\sqrt{3}; \infty)

(- \infty; 1) \cup (\sqrt{3}; \infty)

1003029003

Level:

Find the solution set of the inequality.

(x^{3} + 8) (x^{4} + 1) (x - 3) < 0

(- 2; 3)

(- \infty; - 2) \cup (3; \infty)

(- 2; \infty)

(- \infty; - 2) \cup (- 1; 1) \cup (3; \infty)

1003029004

Level:

Find the solution set of the inequality.

x^{4} - 1 \geq 0

(- \infty; - 1] \cup [1; \infty)

[- 1; 1]

R

[1; \infty)

1003029005

Level:

Find the solution set of the inequality.

(2 x^{2} - 18) (x^{3} - 8) < 0

(- \infty; - 3) \cup (2; 3)

(- 3; 2) \cup (3; \infty)

(- 3; 3)

(- \infty; - 3)

1003029006

Level:

Find the solution set of the inequality.

(x^{4} + 1) (x^{2} + 4) < 0

\emptyset

(- \infty; - 2) \cup (2; \infty)

(- 2; - 1) \cup (1; 2)

(- 1; 1)

1003189101

Level:

Find the sum of all the positive real roots of the given equation.

x^{4} - 116 x^{2} + 1600 = 0

14

116

0

16

1003189102

Level:

Find the product of all the negative real roots of the given equation.

x^{4} - 34 x^{2} + 225 = 0

15

The equation has no negative real roots.

225

- 34

Higher degree equations and inequalities

9000019807

9000025805

9000028306

1003029002

1003029003

1003029004

1003029005

1003029006

1003189101

1003189102

Events

Akce

Interests

Zajímavosti

About portal

O portálu