Quadratic equations and inequalities

9000020409

Level:

One of the solutions of the quadratic equation

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

x_{1} = 5

. Find the second solution

x_{2}

and the value of the coefficient

b

x_{2} = - 2

and

b = - 3

x_{2} = - 3

and

b = - 2

x_{2} = 2

and

b = 3

x_{2} = 3

and

b = 2

9000020410

Level:

The quadratic equation

a x^{2} + 4 x + c = 0

has solutions

x_{1} = - 3

and

x_{2} = 5

. Find the coefficients

a

and

c

a = - 2

c = 30

a = - 2

c = - 30

a = 2

c = - 30

a = 2

c = 30

9000020909

Level:

The sum of squares of two consecutive integers is

1201

. Identify these integers.

24

and

25

23

and

24

25

and

26

26

and

27

9000021703

Level:

Solve the following inequality.

(x - 2)^{2} \geq (x + 1) (x - 5)

x \in R

x \in \emptyset

x \in (- \infty; \frac{9}{8}]

x \in [\frac{9}{8}; \infty)

9000021803

Level:

Solve the following inequality.

(3 x - 1) (2 - 4 x) < 0

x \in (- \infty; \frac{1}{3}) \cup (\frac{1}{2}; \infty)

x \in (\frac{1}{3}; \frac{1}{2})

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

x \in (\frac{1}{3}; \infty)

9000022301

Level:

Find the solution set of the quadratic inequality.

x^{2} - 8 x + 16 \leq 0

{4}

\emptyset

R ∖ {4}

R

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

9000022303

Level:

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

(2; 5)

. Determine this inequality.

x^{2} - 7 x + 10 < 0

x^{2} + 7 x + 10 > 0

x^{2} - 7 x + 10 \leq 0

x^{2} + 7 x + 10 \geq 0

x^{2} - 7 x + 10 > 0

9000022304

Level:

Find all the values of

x

at which the following expression attains nonnegative value.

x^{2} + x - 12

x \in (- \infty; - 4] \cup [3; \infty)

x \in [- 3; 4]

x \in [- 4; 3]

x \in (- \infty; - 4) \cup (3; \infty)

x \in (- \infty; - 3] \cup [4; \infty)

9000022805

Level:

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

[3; 5]

. Identify this inequality.

x^{2} - 8 x + 15 \leq 0

x^{2} + 8 x + 15 \leq 0

x^{2} - 8 x + 15 \geq 0

x^{2} + 8 x + 15 \geq 0

9000022806

Level:

For an integer variable

x

find the solution set of the following quadratic inequality.

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

{- 1; 0; 1; 2}

{- 2; - 1; 0; 1}

{0; 1; 2; 3}

{- 3; - 2; - 1; 0}

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Quadratic equations and inequalities

9000020409

9000020410

9000020909

9000021703

9000021803

9000022301

9000022303

9000022304

9000022805

9000022806

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