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

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SUMMARY

The discussion centers on solving the x-intercepts of the function (30x^4 + 23x^3 - 29x^2 + 6x)/x. The user initially simplified the equation incorrectly to 30x^3 + 23x^2 - 29x + 6x, leading to confusion in identifying the correct roots. Using Newton's method with an initial guess of 0 yielded an incorrect approximation of 1/3, while the actual x-intercept is -1.5. The error stemmed from misapplying the division by x, which left a factor of x in the 6x term, and the user was advised to avoid starting Newton's method at a discontinuity.

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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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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.
 

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