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Problem 24 Medium Difficulty

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ x^5 - 3x^4 + x^3 - x^2 + 6 = 0 $

Answer

$x \approx-1.04450307,1.33258315,2.70551209$

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Video Transcript

All right, Question 24. I inflict the graph of the function. Okay, Right over here. X, you won't come on x to the fifth minus three. Exclude the fourth plus X cube minus six. Weird. Minus X plus six. And you can see here that are points of interests are at approximately negative one Negative. I'm sorry. Positive. One white three and 2.7. Now the website will give me the exact number, but Newton's method is too. Um they f of x, er three x and one equals X. And I put this in my graphing calculator minus f of X. Oh, that. So I have my big thanks to him lie in his three x to the fore, plus X cube minus. It's where minus X. Well, six. The derivative. Why this minus Well, X Q Oh, re X minus three X squared minus two X like this one. So in my graphic cab leader, I have this part and oh, that and stare around X negative. And whatever I get out, I'm gonna put in my exit too, until the equal each other. So exit to eat. And I had to go in and change my I had the mode button and changed the decimal eight decimal points s o negative 1.47 6 1905 So that that becomes my new input for ex. So you have to change your table toe ask instead of auto. So to do that, you had the second window button and we'll see an auto, and you wanted to be asked so that you can put in negative one point. Oh, for 761905 and see what you get out for your wife value, and then that's gonna be your next ask. So then you put it in negative 1.0 445 1 74 And then I put batting for my next ass and I get negative for or by 0307 and batting for my next ass, and I get the exact same thing out. So that becomes my exit five. And then that becomes my answer. And when you grab like when I put my graft into the Web site, it gives me the points, and this would be one of the answers. So I do the same thing for 1.3 except one equals 1.3. When I was that in for my ex of one, I get 1.33 three 13 See room for five than accept three becomes 1.33 258 and Daddy 1.33 to five a 316 which are equal Exit five. And then when I do it for 1.7 seven. Handsome too. When I put in 2.7, I get 2.7. We're 55 6135 But then for my ass and I get people seven. They can see it in merging 1210 exit for more seven 10 And that also equals except five. So that's where converged and that would be.