Solving the Quadratic Equation: x^2 - 5x >= 0

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SUMMARY

The discussion focuses on solving the quadratic inequality x^2 - 5x >= 0. The solution involves factoring the expression into x(x - 5) = 0, yielding critical points at x = 0 and x = 5. These points divide the number line into three intervals, allowing for testing of values within each interval to determine where the inequality holds true. The conclusion is that the solution set includes x ≤ 0 and x ≥ 5.

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  • Familiarity with the Quadratic Formula
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  • Ability to analyze intervals on a number line
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Homework Statement



How would you solve this problem:

x^2 - 5x >= 0


Homework Equations





The Attempt at a Solution



I think it might be something to do with the Quadratic Formula?
 
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Look at it as two problems: x^2 - 5x = 0 and x^2 - 5x > 0. For the first problem, the simplest way is to factor the quadratic expression, which will give you two solutions. These two numbers divide the number line into three regions. Pick one value in each region and determine whether it satisfies the inequality. If one number in a region satisfies the inequality, every number in the region will satisfy it.
 
It should be fairly clear that x^2- 5x= x(x- 5). Once you have done that you can use the facts that "positive times positive is positive" and "negative times negative is positive".
 

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