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

[Albert]

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

 

[MathLover1]

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

 

[Albert]

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
View attachment 2669
View attachment 2670
View attachment 2671



View attachment 2672

View attachment 2673

View attachment 2674


checking all above, we see that
View attachment 2676
View attachment 2677
View attachment 2678-> 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

 

[Albert]

Thanks a lot for taking time to solve it
Like you I also use Newton's method to solve ,I also write a program (excel)
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
View attachment 2690

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

 

[Albert]

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

 

[Albert]

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

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

 

[Albert]

sorry
You are right
I mistype the fuction 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

 

[Albert]

　MathLover 1 You are right 　 　
So wonderfiu
Thank you very much　 　 　 　 　 　 　 　 　

 

[Albert]

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