Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

2, -4, and 1 + 3i

Answer 1

ok so i know that it will look like

(x-2)(x+4)(x+(1+3i))(x-(1+3i))

but i don't know how to factor the last half

Answer 2

(x^2+2x-8)(x+(1+3i))(x-(1+3i))

Answer 3

@precal

Answer 4

you need to expand it, do you know how to work with complex numbers

Answer 5

sorta, i know how to do it but i never get the answer right

Answer 6

no your complex solutions are 1+3i and 1 - 3i

Answer 7

those are your conjugates

Answer 8

well, now i know why i always get it wrong...

Answer 9

(1+3i)(1-3i)
1^2+3i-3i-9i^2
1-9i^2
1-9(-1)
1+9
10
I think it is x^2-10

Answer 10

let me think about this........

Answer 11

not x^2-10

Answer 12

f(x) = x4 - 2x2 + 36x - 80

f(x) = x4 - 3x3 + 6x2 - 18x + 80

f(x) = x4 - 9x2 + 36x - 80

f(x) = x4 - 3x3 - 6x2 + 18x - 80

these are the possible answers

Answer 13

that doesn't help

Answer 14

x^2+10=0
using quadratic formula
a=1 b=0 c=10

Answer 15

x=-0+square root of (0^2-4(1)(10) ) all over 2(1)
x=square root of -40 all over 2
\[\frac{ \sqrt{-40} }{ 2 }\]

Answer 16

Let me go look at some of my old classnotes, be right back

Answer 17

ok, thank you

Answer 18

oh wow this one is in my book

Answer 19

[x-(1+3i)][x-(1-3i)] they expanded this out
[x-1-3i][x-1+3i]
[(x-1)-(3i)][(x-1)+(3i)] do you see the difference of squares (a-b)(a+b)?

Answer 20

[(x-1)^2-9i^2]
x^2-2x+1-9i^2
note i^2 is -1
x^2-2x+1-9(-1)
x^2-2x+1+9
x^2-2x+10 ok so now multiply this to your other two

Answer 21

you can always verify that this is true by solving for x using the quadratic formula

Answer 22

ok, thank you :)

Answer 23

yw