Chapter 3 Roots Of Polynomials

Question 1

What is the relationship between the roots a and b of the quadratic equation az² + bz + c = 0?

Answer 1

a + b = -b

a * b = c

Question 2

What is the relationship between the roots a, b, and y of the cubic equation az³ + bz² + z + d = 0?

Answer 2

If a, b, and y are the roots, then a + b + y = - (coefficient of z²)

a * b + b * y + a * y = coefficient of z

Question 3

What are the roots of the quartic equation az^4 + bz^3 + cz^2 + dz + e = 0?

Answer 3

α, β, γ, δ

Question 4

What is the sum of the roots (Sα) of the quartic equation?

Answer 4

Sα = α + β + γ + δ = -b/a

Question 5

What is the sum of the products of the roots taken two at a time (Eαβ)?

Answer 5

Eαβ = αβ + αγ + αδ + βγ + βδ + γδ = c/a

Question 6

What is the sum of the products of the roots taken three at a time (Eαβγ)?

Answer 6

Eαβγ = αβγ + αβδ + αγδ + βγδ = -d/a

Question 7

What is the product of the roots (Eαβγδ)?

Answer 7

Eαβγδ = αβγδ = e/a

Question 8

What notation is used to summarize the formulae for elementary symmetric functions?

Answer 8

siama notation

Question 9

How many roots does a polynomial equation of degree n have?

Answer 9

A polynomial equation of degree n has n roots, including complex and repeated roots.

Question 10

What is true about complex roots in polynomial equations with real coefficients?

Answer 10

Complex roots always occur in conjugate pairs.