Solving polynomial equations ,f(x)=x³+4x-6

y=f(x) is a polynomial
let f(x)=x³+4x-6
find all the solutions of x making f(x)=0

 

first graph x^3+4x-6=0 to see where zeros are approximately


so, there will be one real zero, between 1 and 1.5

use Newton’s Method to find zero

f(x)=x^3+4x-6
first derivative is
f'(x)=3x^2+4


let initial value x₀=0













checking all above, we see that


-> closest to zero

so, solution is x[0]=1.135

 

Thanks a lot for taking time to solve it
Like you I also use Newton's method to solve ,I also write a program (excell)
to solve ,and I find 3 solutions two negative and one positive
positive solution:x=1.6739
negative solutions: x=-0.917 and x=-3.257

 

i write a program using excel to solve the question
I must put into a seed first
when i keey in 1 I get x=1.673
i keey in -1 I get x=-0.917
I keey in -3 I get x=- 3.257

 

Using Newton's method
I write a program using excel to solve the question
I must put into a seed first
when I keey in 1 I get x=1.673
I keey in -1 I get x=-0.917
I keey in -3 I get x=- 3.257
You may take a reference of the graph shown below

 

sorry
You are right
I mistype the fuctionn in my program
I try again with the right function and put in the seed 1
and I get the solition x=1.1347

 

from the graph there is only one solution
sorry again

 

　MathLover 1 You are right 　 　
So wonderfiu
Thank you very much　 　 　 　 　 　 　 　 　

 

x ~ 1.1347 is the only solution
MathLover 1 Your answer is correct
Thank you very much