Solving X-Intercepts of 30x^4+23x^3-29x^2+6x/x

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In summary, the function given is (30x^4+23x^3-29x^2+6x)/x, which can be simplified to 30x^3+23x^2-29x+6. The first guess for Newton's method was set to 0, which resulted in an approximation of 1/3 as a root. However, when using Graphmatica, the curve did not pass through this point but instead through -1.5. This may be due to the first guess lying on a discontinuity in the graph and the equation being incorrectly entered into the program. The correct roots are -3/2 and 1/3.
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SwAnK
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hey, I was given this function to analyze, and when it came to the x-intercepts i think i must be getting confused. The equation is (30x^4+23x^3-29x^2+6x)/x which i made into 30x^3+23x^2-29x+6x to make it easier to work with.

Anyways i used Newton's method and let my first value =0 to approximate a root and came out with 1/3. However when i used graphmatica, the curve does not pass through this point at all, but -1.5. THe weird thing is that both these points, when subbed into the equation equal zero. Where am I messing this up? thanx
 
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6x / x is not 6x. Also, you may not want to make your first guess for Newton's method lie on a discontinuity in the graph. Thirdly, according to descartes rule of signs that function should have over 1 real root. You probably botched plugging it into the program.
 
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  • #3
When you divided by x you left a factor of x in the 6x term. It should just be x.

However, you do have the right roots (-3/2, 1/3 and I'll leave the third to you!) so I suspect you entered the equation into Graphmatica incorrectly.
 

1. What is the formula for finding the x-intercepts of a polynomial function?

The formula for finding the x-intercepts (or roots) of a polynomial function is to set the function equal to zero and then solve for x. In other words, the x-intercepts are the values of x for which the function equals zero.

2. How do I solve for x-intercepts when the function has a degree higher than 2?

To solve for x-intercepts of a polynomial function with a degree higher than 2, you can use the Rational Root Theorem or synthetic division to find the possible rational roots. Then, use the remainder theorem to test these possible roots and determine the actual roots.

3. Can I use a graphing calculator to find the x-intercepts of a polynomial function?

Yes, you can use a graphing calculator to find the x-intercepts of a polynomial function. Simply graph the function and look for the points where the graph crosses the x-axis, which indicates the x-intercepts.

4. What is the difference between x-intercepts and solutions of a polynomial function?

The x-intercepts of a polynomial function are the values of x for which the function equals zero. On the other hand, the solutions of a polynomial function are the values of x for which the function equals a specific value, not necessarily zero.

5. Are there any shortcuts or tricks to finding the x-intercepts of a polynomial function?

There are a few shortcuts and tricks that can make finding x-intercepts of a polynomial function easier, such as using the rational root theorem, synthetic division, or factoring the function. However, these methods may not always work, and it is important to understand the underlying concepts of finding x-intercepts.

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