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aew782
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I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
Cubic non-linear inequality (HELP)
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In summary, the conversation discusses difficulty with a question from a review test that involves finding the zeros of a cubic expression and analyzing an inequality. The suggested method is to decompose the expression and plot it graphically, checking the quality of the inequality for each interval on the x-axis. The Rational Root theorem is not applicable in this case.
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SteamKing
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I don't see any inequality.
As far as expressing the equation graphically, you just plot it.
As far as expressing the equation graphically, you just plot it.
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symbolipoint
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aew782 said:I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
Try to decompose the cubic expression to find the zeros, meaning find if possible its linear and any quadratic factors (if quadratic factor cannot be factored further). It may have as many as three zeros, but not more. The function (now being equal to zero) is in possibly four intervals. You don't show us the direction of your inequality but you say you want to analyze the inequality; but anyway, you check the quality of the value of the "inequality" for each interval of the x-axis and determine if the x value is true for the inequality or false.
EDIT: harder than I thought. +1 is not a root and -1 is not a root. Rational Root theorem will not work.
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CellCoree
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I understand that tackling complex equations and inequalities can be challenging. In order to solve a cubic non-linear inequality, it is important to first understand its properties and characteristics. A cubic function is a polynomial of degree three, meaning it has three terms with the highest degree being three. Non-linear means that the function is not a straight line.
To express a cubic non-linear inequality graphically, you can plot the function on a graph and shade the region that satisfies the inequality. The points within the shaded region are the solutions to the inequality. This can help you visualize the solution and better understand the behavior of the function.
Algebraically, you can solve a cubic non-linear inequality by using techniques such as factoring, the quadratic formula, or completing the square. It is important to be familiar with these methods and choose the one that is most suitable for the given inequality.
If you are still struggling with a specific question from your review test, I recommend seeking help from a teacher, tutor, or classmate. Working through the problem with someone else can provide a fresh perspective and help you understand the concept better.
Remember, solving equations and inequalities takes practice and patience. Keep persevering and seeking help when needed, and you will be able to master the concept of cubic non-linear inequalities.
1. What is a cubic non-linear inequality?
A cubic non-linear inequality is an inequality that includes variables raised to the power of three or higher, and cannot be rearranged to form a straight line. These inequalities can have multiple solutions and often require graphing to find the solution set.
2. How do I solve a cubic non-linear inequality?
To solve a cubic non-linear inequality, you can use a variety of methods such as graphing, substitution, or factoring. Depending on the specific inequality, some methods may be easier or more efficient than others. It is important to carefully follow the steps and check your solution to ensure its accuracy.
3. What is the difference between a cubic non-linear inequality and a cubic equation?
A cubic non-linear inequality involves an inequality symbol (<, >, ≤, or ≥) and has multiple possible solutions, while a cubic equation involves an equal sign (=) and has only one solution. In other words, a cubic non-linear inequality represents a range of values, while a cubic equation represents a single value.
4. Can a cubic non-linear inequality have more than one solution?
Yes, a cubic non-linear inequality can have multiple solutions. This is because the inequality symbol allows for a range of values to be considered as solutions, rather than just one specific value.
5. How can I check my solution to a cubic non-linear inequality?
To check your solution to a cubic non-linear inequality, you can substitute the values you found into the original inequality and see if it satisfies the inequality. You can also graph the inequality and see if the solution falls within the shaded region.
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