Recipe Cards

Question 1

what are the general steps when trying to solve for a co-efficent in the polynomial equation?

Roots of polynomials

Answer 1

1. write out a=, b=, c=, d=, e=…..
2. then write out the roots α=, β=, γ=,δ=
3. write out general formulas with co effiecnt equivelent
4. see which equations would utilise co efficents that we nned to find
5. substitute the roots into the equation and solve for the co efficents

Question 2

What are the general steps when trying to solve for a root(s) of the polynomial equation?

Roots of Polynomials

one has been given

Answer 2

1. If the given root is complex- the other must be a conjugate of this (conjugate pairs)
2. write out a=, b=, c=, d=, e=…..
3. then write out the roots α=, β=, γ=,δ=
4. write out the general formulas
5. look secifically first at Σα and Σαβγδ as these involve less algebra, but sometimes sadly this inevitable
   6.

Question 3

what is the quickest way to find the roots of a quadratic?

Answer 3

1. Define a,b,c
2. set up the quadratic formula
3. check answer in equation solver

Question 4

What does it mean when it says “solve the equation f(z) =0” ?

Answer 4

It’s asking for the real roots of the equation
Whenever it says “solve” give a conclusion statement at the end stating ALL the roots

Question 5

how would you set up a quartic/ cubic equation if given all the roots?

Answer 5

1. turn 2 of the roots into a quadratic equation using z^2-(α+β)z+ (αβ)
2. by inspection detrmine the other quadratic/ factor
3. multiply the two out to give a final equation

Question 6

when given an equation, how would you find the equation of equation whose roots are manipulated?
eg: 2α+1

Answer 6

1. if f(z)=0 and f(2z+1) is equal to 0
2. give the intial equation root the value of w
3. then eqate w to the manipulated root
4. solve for z
5. then substitute this into the main equation in place for w