Quadratic equations and inequalities

9000022807

Level:

Complete the following statement: Quadratic inequality

2 x^{2} - 3 x + 4 > x^{2} + 2 x - 2

is satisfied if and only if

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

x \in (2; 3)

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

x \in (- 2; - 3)

9000022808

Level:

Find all the real values of

x

which ensure that the following expression is negative.

- x^{2} + 4 x - 4

x \in R ∖ {2}

none

x

with this property

x = 2

x \in R

9000022809

Level:

Find the solution set of the following quadratic inequality.

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

\emptyset

R

{\frac{1}{2}}

{- \frac{1}{2}}

9000022810

Level:

Find the solution set of the following quadratic inequality.

- x^{2} + 2 x + 3 > 0

(- 1; 3)

(- \infty; - 1)

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

(3; \infty)

9000033701

Level:

Find out, how many integer solutions the following inequality has.

m^{2} + 2 m - 4 < 0

Five integer solutions.

Less than five integer solutions.

9000034905

Level:

The solution set of one of the following quadratic inequalities is the interval

[- \frac{7}{6}; \frac{3}{4}]

. Determine this inequality.

(x + \frac{7}{6}) (x - \frac{3}{4}) \leq 0

(x + \frac{7}{6}) (x - \frac{3}{4}) \geq 0

(x - \frac{7}{6}) (x + \frac{3}{4}) \geq 0

(x - \frac{7}{6}) (x + \frac{3}{4}) \leq 0

9000034906

Level:

The solution set of one of the following quadratic inequalities is

(- \infty; - \frac{3}{5}) \cup (\frac{1}{6}; \infty)

. Determine this inequality.

(5 x + 3) (1 - 6 x) < 0

(5 x - 3) (6 x + 1) < 0

(5 x + 3) (1 - 6 x) > 0

(5 x - 3) (6 x + 1) > 0

9000034907

Level:

Find all

x \in R

for which the following expression takes nonnegative values.

- 2 (x - 3) (2 - x)

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

[2; 3]

(2; 3)

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

9000034908

Level:

Find all

x \in R

for which the following expression is nonpositive.

(x + 1) (4 + x)

[- 4; - 1]

(- \infty; - 4] \cup [- 1; \infty)

(- 4; - 1)

(- \infty; - 4) \cup (- 1; \infty)

9000034909

Level:

Find the solution set of the following quadratic inequality.

- 3 (x + 2)^{2} < 0

R ∖ {- 2}

\emptyset

{- 2}

R

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Quadratic equations and inequalities

9000022807

9000022808

9000022809

9000022810

9000033701

9000034905

9000034906

9000034907

9000034908

9000034909

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