Equations and inequalities with parameters

9000033704

Level:

Find the values of real parameter

p

which ensure that the following quadratic equation has solutions with nonzero imaginary part.

p x^{2} + 4 x - p + 5 = 0

p \in (1; 4)

p \in [1; 4]

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

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

9000034701

Level:

Identify a set of the values of the real parameter

m

which ensure that the equation

\frac{m}{x} - 8 = \frac{1}{x} - \frac{m + 3}{2}

has solution

x = 2

{7}

{10}

{6}

{\frac{5}{2}}

9000034702

Level:

Identify the set of the values of the real parameter

d

for which the following equation has no solution in

R

x^{2} - 2 d x + 2 d^{2} - 9 = 0

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

(- 3; 3)

(3; \infty)

(- \infty; - 3)

9000034703

Level:

Identify the set of the values of the real parameter

t

for which the following equation has two different real roots.

x^{2} + (t + 2) x + 1 = 0

(- \infty; - 4) \cup (0; \infty)

(- \infty; - 4)

(- 4; 0)

(0; \infty)

9000034704

Level:

Solve the inequality

a x - 2 > 0

with a real unknown

x

and a nonpositive real parameter

a < 0

(- \infty; \frac{2}{a})

(- \infty; - \frac{2}{a})

(\frac{2}{a}; \infty)

(- \frac{2}{a}; \infty)

9000034705

Level:

Solve the inequality

2 x + b > 0

with a real unknown

x

and a real parameter

b \in R

(- \frac{b}{2}; \infty)

(\frac{b}{2}; \infty)

(- \infty; \frac{b}{2})

(- \infty; - \frac{b}{2})

9000104301

Level:

Assuming

a < 0

, solve the following inequality.

3 x + 2 a \geq 0

[- \frac{2 a}{3}; \infty)

(- \infty; - \frac{2 a}{3}]

(- \infty; - \frac{2 a}{3})

(- \frac{2 a}{3}; \infty)

9000104303

Level:

Assuming

a < 3

, solve the following inequality.

a x - 3 \geq 3 x - a

(- \infty; - 1]

(- \infty; - 1)

(- 1; \infty)

R

9000104304

Level:

Assuming

a < 0

, solve the following inequality.

\frac{x}{a} \geq 1

(- \infty; a]

(- \infty; a)

[a; \infty)

(a; \infty)

9000104305

Level:

Assuming

a > - 1

, solve the following inequality.

\frac{2 x}{a + 1} - 1 < 0

(- \infty; \frac{a + 1}{2})

(- \frac{a + 1}{2}; \frac{a + 1}{2})

{\frac{a + 1}{2}}

(\frac{a + 1}{2}; \infty)

Equations and inequalities with parameters

9000033704

9000034701

9000034702

9000034703

9000034704

9000034705

9000104301

9000104303

9000104304

9000104305

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