Math Problem Statement
Which of the following sets are equal? 2. π΄ = {1, 2, 3},π΅ = {π₯; π₯^2 β 2π₯ + 1 = 0}, πΆ = {π₯; π₯^3 β 6π₯^2 +11π₯ β6 = 0}.
Solution
To determine which sets are equal, let's analyze the sets individually:
Set :
Set :
Factorizing the quadratic equation: Thus, the solution is: So:
Set :
Factorizing the cubic equation: The solutions are: Thus:
Comparing the Sets:
Conclusion:
Final Answer:
The sets and are equal.
Would you like detailed explanations of the factorization steps or have any related questions? Here are some related questions to deepen your understanding:
- How do you determine the roots of a cubic equation?
- Can you explain how to factorize higher-degree polynomials systematically?
- Why is a perfect square trinomial?
- What are some real-world applications of solving polynomial equations?
- How can the equality of sets be determined in more complex scenarios?
Tip: Always verify your solutions by substituting the roots back into the original equation.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Algebra
Factorization of Polynomials
Formulas
Factoring a quadratic equation: x^2 - 2x + 1 = (x - 1)^2
Factoring a cubic equation: x^3 - 6x^2 + 11x - 6 = (x - 1)(x - 2)(x - 3)
Theorems
Roots of Polynomial Equations
Equality of Sets
Suitable Grade Level
Grades 9-12
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