Question
How to classify 2x^3 + 5x - 2 = 0 as linear or non-linear and why?
Answers
GPT-4o mini
To classify the equation \( 2x^3 + 5x - 2 = 0 \), we need to look at the highest degree of the variable \( x \) in the equation.
In this case, \( 2x^3 \) is the term with the highest degree, which is 3. An equation is classified as:
- **Linear** if it is of the first degree (the highest power of the variable is 1).
- **Non-linear** if the highest degree is greater than 1.
Since the highest degree in the given equation is 3, we can classify the equation \( 2x^3 + 5x - 2 = 0 \) as **non-linear**.
The reason is that it contains a cubic term, which leads to a curve rather than a straight line when graphed. Thus, the equation is non-linear.
In this case, \( 2x^3 \) is the term with the highest degree, which is 3. An equation is classified as:
- **Linear** if it is of the first degree (the highest power of the variable is 1).
- **Non-linear** if the highest degree is greater than 1.
Since the highest degree in the given equation is 3, we can classify the equation \( 2x^3 + 5x - 2 = 0 \) as **non-linear**.
The reason is that it contains a cubic term, which leads to a curve rather than a straight line when graphed. Thus, the equation is non-linear.