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 + 3i
These are the answer choices:
(a)f(x) = x4 - 4x3 + 15x2 + 25x + 150
(b)f(x) = x4 - 9x2 - 50x - 150
(c)f(x) = x4 + 12.5x2 - 50x - 150
(d)f(x) = x4 - 4x3 - 15x2 - 25x - 150

Answer 1

if \(a+bi\) is a zero of a quadratic, the quadratic is
\[x^2-2ax+a^2+b^2\]
what is the quadratic with zeros \(-1+3i\) ?

Answer 2

I'm not sure? @misty1212

Answer 3

in
\[-1+3i\] you get \(a=-1,b=3\) plug those in to \[x^2-2ax+a^2+b^2\]

Answer 4

\[x ^{2}-2(-1)x+(-1)^2+(3)^2\]

Answer 5

ok that is good but then write what it really is

Answer 6

when you compute i mean

Answer 7

\[x^2-2x+10\]

Answer 8

i think you made a mistake on the second part
two minus signs make it plus

Answer 9

\[x^2+2x+10\]

Answer 10

alright so what now?

Answer 11

@misty1212

Answer 12

then multiply this by
\[(x-5)(x+3)\] because that will have the zeros you want

Answer 13

\[(x-5)(x+3)(x^2+2x+10)\] you have to multiply all this ugly mess out
maybe we can cheat a bit

Answer 14

http://www.wolframalpha.com/input/?i=%28x-5%29%28x%2B3%29%28x^2%2B2x%2B10%29

Answer 15

\[x^4-9x^2-50x-150?\]

Answer 16

\[x^4-9 x^2-50 x-150\]accoring to wolfram
look at the zeros and see that they are the ones you want

Answer 17

well I think I see it all but where is 3i?

Answer 18

I take it back I see nothing