Question

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

5, -3, and -1 + 2i

Answer 1

sorry it went away

Answer 2

oh ok

Answer 3

before we begin is it clear that two factors are \((x-5)\) and \((x+3)\)?

Answer 4

yes

Answer 5

ok so the real job (before multiplying out) is the find the quadratic polynoimial with zeros at \(-1+2i\) and its conjugate \(-1-2i\)

Answer 6

you want the easy way, or the real real easy way?

Answer 7

real real easy

Answer 8

ok actually lets to the easy way first then the real real easy way

Answer 9

we can work backwards starting with
\[x=-1+2i\] add 1 and get
\[x+1=2i\] then square (carefully) to get
\[(x+1)^2=(-2i)^2\] or
\[x^2+2x+1=-4\]

Answer 10

add 4 to both sides and get
\[x^2+2x+5=0\] and that is your polynomial

Answer 11

the real real easy way requires memorizing something
that if \(a+bi\) is a zero of a quadratic, then it is
\[x^2-2ax+(a^2+b^2)\] so in your case \(a=-1,b=2\) and the quadratic is
\[x^2-2\times (-1)x+(-1)^2+2^2\] i.e.
\[x^2+2x+5\]

Answer 12

those arent any options tho :(

Answer 13

your final job is to multiply \[(x-5)(x+3)(x^2+2x+5)\]

Answer 14

if it was me, i would cheat so as not to screw up the algebra when multiplying

Answer 15

you know how to do that?

Answer 16

wait let me try again

Answer 17

ok i will leave you to it, then show you how to get the answer for sure

Answer 18

yeah the answer i get does not match up with my choices

Answer 19

http://www.wolframalpha.com/input/?i=%28x-5%29%28x%2B3%29%28x^2%2B2x%2B5%29

Answer 20

see if that one does

Answer 21

Oh thank-you! maybe i was multiplying something wrong!

Answer 22

that is why i said "cheat" is is easy to make a mistake when multiplying all this muck out

Answer 23

yw