Newton-Raphson Formula question

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The discussion centers on finding the smallest positive root of the equation x^4 + x^2 - 80= 0 using the Newton-Raphson method. A suggested starting point for the iteration is x = 3, which is considered appropriate for the problem. Participants note that the equation can be solved analytically, making the use of Newton-Raphson unnecessary. However, the original poster confirms their understanding of both the equation's solvability and the application of the method. The conversation emphasizes the balance between analytical solutions and numerical methods in solving equations.
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Question:
Find the smallest positive root of the equation x^4 + x^2 - 80= 0 correct to two decimal places. Use the Newton-Raphson process.

How would I go about finding the smallest positive root? What I was thinking is using x = 3 as x = 3 is the largest number that would be close to 0 (for the equation), then finding an approximation for that, is that correct?

thanks.
 
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1) Independent of the question asked, can you see that the equation is trivially solvable exactly analytically (no need for Newton-Raphson)?

2) For a numeric solution, a start value of 3 looks fine. I assume (hope) you know how to apply Newton-Raphson from there.
 
Last edited:
PAllen said:
1) Independent of the question asked, can you see that the equation is trivially solvable exactly analytically (no need for Newton-Raphson)?

2) For a numeric solution, a start value of 3 looks fine. I assume (hope) you know how to apply Newton-Raphson from there.

I'm perfectly aware it is solvable from that form, and I do know how to apply Newton-Raphson. Thanks.
 

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