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Hence, explain how you know that [tex]x^2 - 8x + 20[/tex] is always positive.

Complete the square:

[tex]x^2 - 8x + 20[/tex]

Completing the Square - Basics

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Final answer:

To demonstrate that x² - 8x + 20 is always positive, completing the square reveals that the expression simplifies to a square term plus a positive constant.


Explanation:

To show that the expression x² - 8x + 20 is always positive, we can complete the square. The given expression can be rewritten as (x - 4)² + 4. Since any square term is always non-negative, and adding a positive constant to it keeps it positive, we conclude that x² - 8x + 20 is always positive.


Learn more about Completing the square to analyze the positivity of quadratic expressions here:

https://brainly.com/question/40644823


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