Question

Form a polynomial f(x) with real co-efficients having the given degree and zeros.

a. Degree 4; zeros: -5-5i; multiplicity 2
b. Degree 5; zeros: -5; -i-7i+i
c. Degree 4; zeros: 5; multiplicity 2;2i

Answer 1

if -5-5i is a root, then so is -5+5i because complex roots come in conjugate pairs

Answer 2

each roots is of multiplicity 2

Answer 3

so you have something like

(x - (-5-5i) )^2 * (x - (-5+5i) )^2

Answer 4

this is for part a)

Answer 5

would i distribute the negative?

Answer 6

yes you would

Answer 7

i distributed it and it said it was wrong and it changed the first part of the problem to Degree 4; zeros 2+4i; 5; multiplicity 2... would i just follow the same steps

Answer 8

2+4i is a zero so 2-4i is a zero

5 is a root of multiplicity two, so (x-5)^2 is a factor

Answer 9

2+4i is a zero ---> (x - (2+4i)) is a factor

2-4i is a zero ---> (x - (2-4i)) is a factor