Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i
\(f(x) = x^4 - 362.5x^2 + 1450x - 4984\)
\(f(x) = x^4 - 9x^3 + 32x^2 - 725x + 4984\)
\(f(x) = x^4 - 67x^2 + 1450x - 4984\)
\(f(x) = x^4 - 9x^3 - 32x^2 + 725x - 4984\)

Answer 1

I came up with \(x^4+20x^3+133x^2+330x-4984\) but that isnt one of the options

Answer 2

@amistre64

Answer 3

by descartes rule of signs, only one would have a possible chance to work

Answer 4

f(x)=x4−362.5x2+1450x−4984; 3 or 1 +root
f(-x)=x4−362.5x2-1450x−4984; 1 -root

f(x)=x4−9x3+32x2−725x+4984; 4 or 2 or 0 +root, doesnt fit
f(-x)=x4+9x3+32x2+725x+4984

f(x)=x4−67x2+1450x−4984 3 or 1 +root
f(-x)=x4−67x2-1450x−4984; 1 -root

f(x)=x4−9x3−32x2+725x−4984; 3 or 1 +root
f(-x)=x4+9x3−32x2-725x−4984; 1 -roots

i guess we can omit one of them ... thought only one of them had the goods tho

Answer 5

might as well just work the product of the roots

(-14-x)(4-x)(5+8i-x)(5-8i-x)

http://www.wolframalpha.com/input/?i=%28-14-x%29%284-x%29%285%2B8i-x%29%285-8i-x%29

Answer 6

but I want to know what I did wrong?

Answer 7

then i would have to see your work

Answer 8

I did (x+5-8i)(x+5+8i) and came up with \((x^2+10x+89)\) and then (x-4)(x+14) and came up with \((x^2+10x-56)\)

Answer 9

then multiplied them

Answer 10

your complex roots are in error then

Answer 11

you worked x+r in stead of x-r

Answer 12

so it should be x-5-8i and +8i then?

Answer 13

yep

Answer 14

thats why when i do these i subtract x from a root, its just simpler

Answer 15

(r-x) = 0 when x=r just as well as (x-r)

Answer 16

ok thank you so much!

Answer 17

youre welcome