What Methods Identify Nonnegative Ranges in Cubic Equations?

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In summary, a cubic equation is a polynomial equation of the third degree that can be written in the form ax^3 + bx^2 + cx + d = 0. The general method for solving a cubic equation involves factoring, using the cubic formula, or using numerical methods. To factor a cubic equation, the rational root theorem and synthetic division or long division can be used. The cubic formula is a mathematical formula derived from the quadratic formula and can be used to solve cubic equations that cannot be factored. Other methods for solving cubic equations include Cardano's method and Ferrari's method, which involve complex numbers and may be more complicated.
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danielp3
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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.
 
  • #4
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?
 
Last edited:

Related to What Methods Identify Nonnegative Ranges in Cubic Equations?

1. What is a cubic equation?

A cubic equation is a polynomial equation of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and x is the variable. It has a maximum of three solutions.

2. How do I know if an equation is a cubic equation?

An equation is considered a cubic equation if the highest exponent of the variable is 3. For example, x^3 + 2x^2 + x - 5 = 0 is a cubic equation, while x^2 + 3x + 1 = 0 is not.

3. What is the general method for solving a cubic equation?

The general method for solving a cubic equation is by using the cubic formula, which is x = (-b ± √(b^2 - 4ac - 3a^2) / 2a. However, this method can be quite complex and time-consuming, so there are other methods such as factoring and using the rational roots theorem that are often used instead.

4. Can all cubic equations be solved?

Yes, all cubic equations can be solved. However, some equations may have complex or irrational solutions, which may not be easily calculable.

5. Are there any tips for solving cubic equations?

One helpful tip is to first try to factor the equation to see if any solutions can be easily found. Another tip is to use the rational roots theorem to narrow down the possible solutions. It may also be useful to work with a graphing calculator or software to visualize the equation and its solutions.

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