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

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

1. ### Albert

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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

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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=1.135

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MathLover1, Apr 22, 2022
Albert likes this.

3. ### Albert

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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

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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

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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:

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Albert, Apr 23, 2022
6. ### Albert

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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

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from the graph there is only one solution
sorry again Albert, Apr 23, 2022
8. ### Albert

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MathLover 1 You are right
So wonderfiu Thank you very much

Albert, Apr 23, 2022
9. ### Albert

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

Albert, Apr 23, 2022