Math Problem Statement
Solution
The image contains mathematical problems in Polish. Here's a summary of each:
- Zadanie 34: Prove that the equation has a solution for every value of .
- Zadanie 35: Prove that there is no value of the parameter such that the equation has a solution in the set of real numbers.
- Zadanie 36: Determine the number of solutions of the equation depending on the value of the parameter .
- Zadanie 37: Find all values of the parameter for which the inequality has no solutions.
- Zadanie 38: Find all values of the parameter for which the derivative of the function is defined in the set of real numbers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Inequalities
Real Numbers
Function Domains
Formulas
Quadratic equation: ax^2 + bx + c = 0
Discriminant: Δ = b^2 - 4ac
Inequality solving techniques
Function domain rules for square roots
Theorems
The quadratic formula: x = (-b ± √Δ) / 2a
Conditions for real roots of a quadratic equation (Δ ≥ 0)
Domain definition for square root functions
Suitable Grade Level
Grades 10-12
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