Math Problem Statement
What is the solution set of the quadratic inequality 4(x + 2)^2 ≤ 0?
Solution
Let's solve the quadratic inequality .
Step-by-step solution:
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Simplify the inequality:
The expression can be rewritten as:
Divide both sides by 4:
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Interpret the inequality:
- The square of a real number is always non-negative, meaning for all .
- The only way is if , which gives .
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Conclusion:
The inequality holds only when . For any other value of , will be positive, and thus the inequality would not hold.
Thus, the solution set is .
Answer:
The correct answer is the first option: .
Would you like more details or have any questions? Here are 5 related questions to expand on this:
- How would the solution change if the inequality were ?
- What are the general steps to solve quadratic inequalities?
- How would you solve ?
- What is the difference between solving an inequality and an equation?
- Can the inequality have more than one solution?
Tip: Always remember that the square of any real number is non-negative. This fact is key in solving many quadratic inequalities.
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Math Problem Analysis
Mathematical Concepts
Quadratic Inequalities
Algebra
Formulas
(x + 2)^2 = 0
Theorems
Non-negativity of squares
Suitable Grade Level
Grades 9-12