Quadratic equations and inequalities

2010007304

Level:

Which of the given sets contains exactly all non-negative integers that satisfy the inequality

\sqrt{(3 x + 6)^{2}} \leq 12

{0; 1; 2}

{0; 1; 2; 3; 4; 5; 6}

{2; 3; 4; 5}

{1; 2}

2010007303

Level:

The area of the rectangle is

735 {cm}^{2}

. Its length is by

14 cm

longer than its width. Find the perimeter of the rectangle.

112 cm

56 cm

252 cm

92 cm

2010007302

Level:

The surface area of a cuboid is

19 942 {cm}^{2}

. Its dimensions are in the ratio

2 : 5 : 7

. Find the volume of the cuboid.

153 790 {cm}^{3}

615 160 {cm}^{3}

76 895 {cm}^{3}

175 760 {cm}^{3}

2010004505

Level:

Find all the values of

x

at which the following expression attains negative value.

2 x^{2} - 7 x - 4

x \in (- \frac{1}{2}; 4)

x \in (- \infty; - \frac{1}{2}) \cup (4; \infty)

x \in (- 4; \frac{1}{2})

x \in (- \infty; - 4) \cup (\frac{1}{2}; \infty)

x \in (- 4; - \frac{1}{2})

2010004504

Level:

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

[- 3; 2]

. Determine this inequality.

x^{2} + x - 6 \leq 0

x^{2} + x - 6 \geq 0

x^{2} - x - 6 \leq 0

x^{2} - x - 6 \geq 0

x^{2} + x + 6 \geq 0

2010004503

Level:

Solve the following inequality.

(5 - 2 x) (7 x + 3) \geq 0

x \in [- \frac{3}{7}; \frac{5}{2}]

x \in [- \frac{5}{2}; \frac{3}{7}]

x \in (- \infty; - \frac{3}{7}]

x \in (\frac{5}{2}; \infty)

2010004502

Level:

The quadratic equation

a x^{2} + b x - 24 = 0

has solutions

x_{1} = - 2

and

x_{2} = 4

. Find the coefficients

a

and

b

a = 3

b = - 6

a = - 3

b = - 6

a = - 3

b = 6

a = 3

b = 6

2010004501

Level:

One of the solutions of the quadratic equation

x^{2} + 7 x + c = 0

x_{1} = - 3

. Find the second solution

x_{2}

and the value of the coefficient

c

x_{2} = - 4

and

c = 12

x_{2} = 4

and

c = - 12

x_{2} = - 4

and

c = - 12

x_{2} = 4

and

c = 12

2000004905

Level:

From the given quadratic equations identify the one that has a double root.

x^{2} - 10 x + 25 = 0

x^{2} - 10 x = 0

x^{2} - 10 = 0

x^{2} - 10 x + 100 = 0

2000004904

Level:

From the given sets identify the one that contains all roots of the quadratic equation:

x^{2} = 5

{- \sqrt{5}; \sqrt{5}}

{0; \sqrt{5}}

{\sqrt{5}}

{- 5; 5}

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Quadratic equations and inequalities

2010007304

2010007303

2010007302

2010004505

2010004504

2010004503

2010004502

2010004501

2000004905

2000004904

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