Roots of Polynomials

Question 1

How can you tell if a polynomial but a quadratic in specific has 2 complex roots

Answer 1

• The discriminant is less than 0
• the coefficients of the polynomial terms are real -This means that the polynomial has a pair of complex conjugate roots

Question 2

What does the law that complex solutions of real polynomials come in pairs

Answer 2

if f(z) = 0 the f(z*) = 0 too.

Question 3

What is meant by the difference of two squares

Answer 3

x^2 - a^2 can be written as (x-a)(x+a)

Question 4

What is meant by the sum of two squares

Answer 4

x^2+a^2 can be written as (x+ai)(x-ai)

Question 5

What’s the form to easily expand 2 complex factors

Answer 5

(x-z)(x-z*) = x^2-2Re(z)x + |z|^2

Question 6

How can |z|^2 be simplified

Answer 6

Re(z)^2 + Im(z)^2

Question 7

What is the equation for the sum of the root (s.o.r)

Answer 7

-b/a

Question 8

What is the equation for the sum of the product pairs (s.o.p.p)

Answer 8

c/a

Question 9

What is the equation for the sum of the product triples (s.o.p.t)

Answer 9

-d/a

Question 10

What is the equation for the product of roots (quartics)

Answer 10

e/a

Question 11

Explain when you can use substitution

Answer 11

If all of the roots are being transformed by the same transformation

Question 12

Explain how to use the substitution method

Answer 12

• let u = the new roots