Quadratic equations and inequalities

9000034909

Level:

Find the solution set of the following quadratic inequality.

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

R ∖ {- 2}

\emptyset

{- 2}

R

9000034910

Level:

Find the solution set of the following quadratic inequality.

(x - 3)^{2} \geq 0

R

\emptyset

R ∖ {3}

{3}

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

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

9000033708

Level:

A stone has been thrown vertically up at the velocity

15 m s^{- 1}

from the initial height

10 m

. How long (in seconds) has been the height of the stone at least

20 m

? Hint: The height

h

is given by the expression

h = s_{0} + v_{0} t - \frac{1}{2} g t^{2}

, the standard acceleration is

g ≐ 10 m s^{- 2}

exactly

1 s

less than

1 s

more than

1 s

The information is not sufficient to give a definite answer.

9000033709

Level:

A square shaped garden with the side

a

should be reduced by a length

x

to another square garden. The difference between the areas of the gardens should not be bigger than

25 %

of the original area. Find the possible values of

x

x \leq a - \frac{\sqrt{3}}{2} a

x \leq \sqrt{3} a

x \leq \frac{3}{4} a

x \leq a + \frac{\sqrt{3}}{2} a

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.

9000025603

Level:

In the following list identify an equation equivalent to the following quadratic equation.

2 (x - 8) (x + \frac{1}{2}) = 0

2 x^{2} - 15 x - 8 = 0

2 x^{2} - 8 x + \frac{1}{2} = 0

8 x^{2} - 15 x + \frac{1}{2} = 0

8 x^{2} - 8 x - 1 = 0

9000025601

Level:

Which of the quadratic equations from the following list has all solutions in the interval

[- 5; 3]

x^{2} - 2 x - 3 = 0

x^{2} - 3 x - 10 = 0

x^{2} - 2 x - 15 = 0

x^{2} - 3 x - 18 = 0

9000025602

Level:

In the following list identify a set which contains at least one solution of the quadratic equation

x^{2} - 121 = 0

{- 11; 1; 13}

{- 5; 0; 5; 10}

{3; 7; 9; 19}

{- 15; - 12; - 7}

Quadratic equations and inequalities

9000034909

9000034910

9000034906

9000034905

9000033708

9000033709

9000033701

9000025603

9000025601

9000025602

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