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

Discussion in 'Algebra' started by Albert, Apr 22, 2022.

1. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
y=f(x) is a polynomial
let f(x)=x³+4x-6
find all the solutions of x making f(x)=0

Albert, Apr 22, 2022
2. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
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

#### Attached Files:

File size:
1.5 KB
Views:
6
MathLover1, Apr 22, 2022
Albert likes this.
3. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
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, Apr 23, 2022
4. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
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, Apr 23, 2022
5. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
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

#### Attached Files:

File size:
20 KB
Views:
5
Albert, Apr 23, 2022
6. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
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, Apr 23, 2022
7. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
from the graph there is only one solution
sorry again

Albert, Apr 23, 2022
8. ### Albert

Joined:
Apr 22, 2022
Messages:
11
0
Location:
Taiwan
MathLover 1 You are right
So wonderfiu
Thank you very much

Albert, Apr 23, 2022

Joined:
Apr 22, 2022
Messages:
11