Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -8, and 2 + 3i

Answer 1

i know i have to multiply (x-4)(x+8) but i dont know what to do about 2+3i

Answer 2

if 2+3i is a root, 2-3i is also a root
cuz complex roots never come single, they always come in conjugate pairs

Answer 3

so you need to multiply below factors also :-

(x-(2+3i))

and

(x-(2-3i))

Answer 4

how do u multiply i's together?

Answer 5

okay, so the required polynomial wud be :-

(x-4)(x+8)(x-(2+3i))(x-(2-3i))

Answer 6

you knw how to deal with first two factors, but u r not sure how to multiply last two factors is it ?

Answer 7

yes

Answer 8

(x-(2+3i))(x-(2-3i))

(x-2-3i)(x-2+3i)

Answer 9

(x-2-3i)(x-2+3i)
--- ----

Answer 10

see that it is of the form (a-bi)(a+bi)
a = x-2
b = 3

Answer 11

is that a formula?

Answer 12

then, simply use this formula : (a-bi)(a+bi) = a^2+b^2

Answer 13

(x-(2+3i))(x-(2-3i))

(x-2-3i)(x-2+3i)

((x-2)^2 + 3^2)

Answer 14

so what is the a^2+b^2 for

Answer 15

thats just a formula,

Answer 16

(x-(2+3i))(x-(2-3i))

(x-2-3i)(x-2+3i)

((x-2)^2 + 3^2)

(x^2 -4x+4+9)

Answer 17

simplify

Answer 18

oh so thats how you multiply them together?

Answer 19

yes !

remember this formula :-
(a+bi)(a-bi) = a^2 + b^2

Answer 20

and dont forget to multiply this with the first two factors
good luck !

Answer 21

i got f(x) = x^4 - 35x^2 + 180x - 416

Answer 22

Excellent !!

wolfram says the same
http://www.wolframalpha.com/input/?i=%28x-%282%2B3i%29%29%28x-%282-3i%29%29%28x-4%29%28x%2B8%29+

Answer 23

thanks

Answer 24

np :)