PERTIDAKSAMAAN SUKU BANYAK - MATEMATIKA PEMINATAN KELAS XI SMA

Introduction

This tutorial focuses on understanding polynomial inequalities, a key topic in mathematics for high school students. It will guide you through the process of solving these inequalities and provide practical examples to reinforce your understanding.

Step 1: Understand Polynomial Inequalities

• A polynomial inequality involves a polynomial expression and an inequality sign (>, <, ≥, ≤).
• The goal is to find the values of the variable that satisfy the inequality.

Key Points:

• Example of a polynomial inequality: ( x^2 - 4 > 0 )
• The polynomial can be factored to find critical points.

Step 2: Identify Critical Points

• Set the polynomial equal to zero to find critical points.
• For ( x^2 - 4 > 0 ):
  • Factor the expression: ( (x - 2)(x + 2) = 0 )
  • Critical points are ( x = 2 ) and ( x = -2 ).

Practical Advice:

• Always check for the potential points where the polynomial changes sign, which are the critical points.

Step 3: Test Intervals

• Divide the number line into intervals based on the critical points.
• For the example ( x^2 - 4 > 0 ), the intervals are:
  • ( (-\infty, -2) )
  • ( (-2, 2) )
  • ( (2, \infty) )

Testing Strategy:

1. Choose a test point from each interval.
2. Substitute the test points back into the inequality to determine if the interval satisfies the inequality.

Step 4: Determine Solutions

• Analyze the results from the test points.
• For ( x^2 - 4 > 0 ):
  • Test point from ( (-\infty, -2) ): Use ( x = -3 )
    • ( (-3)^2 - 4 = 9 - 4 = 5 > 0 ) (True)
  • Test point from ( (-2, 2) ): Use ( x = 0 )
    • ( 0^2 - 4 = -4 > 0 ) (False)
  • Test point from ( (2, \infty) ): Use ( x = 3 )
    • ( (3)^2 - 4 = 9 - 4 = 5 > 0 ) (True)

Conclusion from Testing:

• The solution for ( x^2 - 4 > 0 ) is ( x < -2 ) or ( x > 2 ).

Step 5: Write the Final Answer

• Express the solution in interval notation.
• For the previous example, the final answer is:
  • ( (-\infty, -2) \cup (2, \infty) )

Conclusion

In this tutorial, you learned how to solve polynomial inequalities by identifying critical points, testing intervals, and determining solutions. This process is essential for mastering polynomial functions and prepares you for more advanced topics in mathematics. To further your understanding, practice with different polynomial inequalities and refer to additional resources for more complex examples.