Problem

Use Newton's method to find all the roots of the …

03:24

Problem 29 Easy Difficulty

Use Newton's method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.
$x^{2} \sqrt{2-x-x^{2}}=1$

Answer

$x=-1.97806681$
$x=-0.82646232$

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Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

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Video Transcript

in this trouble were given any question and were asked to use going to Mecca by older whose office separation. So let's start with defining a function that were affects is expert. Well, that's right. That's four x scrape minus X. Afford lunch for or were expert plus one eyes equal to zero. And we What? This function that looks something like this. There are few things that we notice for describe first off, therefore intercepts. And second thing is this. You can see all the powers are even so That means that function is symmetric with respect to t. Why next? So be so only four poles to help. Then be, uh, roots. Undernegative will be the same in magnitude, but opposite in sight. So the intercept are about when? Because it decides 1.9 point agent on the negative side, there to a 0.0.9. And that is important. Eight. So, from this, remember, we need their return for a new cosmetics on this fine new, uh, we find there to that primal thanks to be eight eggs minus for excuse plus eight x over. Expert before squared Now notice methods said that the guest ready a neck situation would be the previous guest minus functional like that. The previous guests divided by the hotel in a second, a previous guest. So let's start with our first does this 0.8 a less black 0.8 for extended this elected function in the day with 3.8. So we find our second guess to be pulling a or two, eh? 7645 And it looks like this. And we find for gas to be about pointing 843108 to 0. And if you plug this thing, be finding four the poor situation to be pointing for everyone here are 8 to 1. And if you like this and we actually find that order approximation is about same as third once on this is definitely one of our rooms. Let's look at the, uh, second rude when nexus point for lane. If you put 0.9 for extend any feel like function of the earth Uh, this point, we find our second guess to be about 1.94 689 Once you're free now, people like this and we find for guys to be 1 49 438 3891 And if it wasn't this, it'd be fine for submission to be about 1.43 age 2538 And we find that the fifth approximation is about Samos, a bird once. All this is definitely also one of our roots. So since we said that dysfunction, it's symmetrical. Suspect Why access and weak inside up roots are plus wing is foreign aid for 3108 to 1 and plus ways both to a negative 1.9438253

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