(4) Roots of Polynomials

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15 Terms

1
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1/α + 1/β =

(α + β)/αβ

2
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1/α + 1/β + 1/γ =

αβ + βγ + αγ/αβγ

3
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1/α + 1/β + 1/γ + 1/δ =

αβγ + βγδ + γδα + δαβ/αβγδ

4
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Roots of a Cubic Polynomial:

α + β + γ

-b/a

5
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Roots of a Cubic Polynomial:

αβ + βγ +αγ

c/a

6
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Roots of a Cubic Polynomial:

αβγ

-d/a

7
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Roots of a Quartic Polynomial:

α + β + γ + δ

-b/a

8
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Roots of a Quartic Polynomial:

αβ + αγ +αδ +βγ + βδ + γδ

c/a

9
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Roots of a Quartic Polynomial:

αβγ + αβδ + αγδ + βγδ

-d/a

10
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Roots of a Quartic Polynomial:

αβγδ

e/a

11
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α² + β² =

(α + β)² - 2αβ

12
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α² + β² + γ² =

(α + β + γ)² - 2(αβ + βγ + αγ)

13
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α² + β² + γ² + δ² =

(α + β + γ + δ)² - 2(αβ + αγ + αδ + βγ + βδ + γδ)

14
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α³ + β³ =

(α + β)³ - 3αβ(α + β)

15
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α³ + β³ +γ³ =

(α + β + γ)³ - 3(α + β + γ)(αβ + βγ + αγ) + 3αβγ