What Methods Identify Nonnegative Ranges in Cubic Equations?

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The discussion focuses on identifying nonnegative ranges in cubic equations, emphasizing the importance of recognizing that the problem presented is an inequality rather than an equation. Participants suggest that factoring the cubic equation can aid in root finding, which is crucial for determining the ranges of t that yield nonnegative values. The conversation highlights the need for users to demonstrate their problem-solving efforts when seeking help. Overall, understanding the relationship between the cubic's roots and its nonnegative intervals is key to solving the posed problem. The thread underscores the importance of proper categorization of mathematical inquiries.
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Poster has been reminded to post schoolwor-type questions in the Homework Help forums, and to show some work on the problem
Summary: Cubic equation

How to solve for t ?

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danielp3 said:
( Poster has been reminded to post school work-type questions in the Homework Help forums, and to show some work on the problem. )
Summary: Cubic equation

How to solve for t ?

View attachment 252728
While we wait for you to show some effort at solving this problem, let me make a point.
That is not an equation. That's an inequality.
 
Following on the last hint, suppose the cubic were factored, equivalent to root finding. How would you tell what ranges of t then produced nonnegative values?
 
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