Topic 4: Roots of Polynomials

Question 1

If α and β are roots of the equation ax²+bx+c=0, what does α+β or Σα equal?

Answer 1

-b/a

Question 2

If α and β are roots of the equation ax²+bx+c=0, what does αβ or Σαβ equal?

Answer 2

c/a

Question 3

If α, β and γ are roots of the equation ax³+bx²+cx+d=0, what does α+β+γ or Σα equal?

Answer 3

-b/a

Question 4

If α, β and γ are roots of the equation ax³+bx²+cx+d=0, what does αβ+βγ+γα or Σαβ equal?

Answer 4

c/a

Question 5

If α, β and γ are roots of the equation ax³+bx²+cx+d=0, what does αβγ or Σαβγ equal?

Answer 5

-d/a

Question 6

If α, β, γ and δ are roots of the equation ax⁴+bx³+cx²+dx+e=0, what does α+β+γ+δ or Σα equal?

Answer 6

-b/a

Question 7

If α, β, γ and δ are roots of the equation ax⁴+bx³+cx²+dx+e=0, what does αβ+αγ+αδ+βγ+βδ+γδ or Σαβ equal?

Answer 7

c/a

Question 8

If α, β, γ and δ are roots of the equation ax⁴+bx³+cx²+dx+e=0, what does αβγ+αβδ+αγδ+βγδ or Σαβγ equal?

Answer 8

-d/a

Question 9

If α, β, γ and δ are roots of the equation ax⁴+bx³+cx²+dx+e=0, what does αβγδ or Σαβγδ equal?

Answer 9

e/a

Question 10

What does α²+β² equal?

Answer 10

(α+β)²-2αβ

Question 11

What does α²+β²+γ² equal?

Answer 11

(α+β+γ)²-2(αβ+βγ+γα)

Question 12

What does α²+β²+γ²+δ² equal?

Answer 12

(α+β+γ+δ)²-2(αβ+γα+αδ+βγ+βδ+γδ)

Question 13

What does α³+β³ equal?

Answer 13

(α+β)³-3αβ(α+β)

Question 14

What does α³+β³+γ³ equal?

Answer 14

(α+β+γ)³-3(α+β+γ)(αβ+βγ+γα)+3αβγ