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) = x4 - 362.5x2 + 1450x - 4984
f(x) = x4 - 9x3 + 32x2 - 725x + 4984
f(x) = x4 - 67x2 + 1450x - 4984
f(x) = x4 - 9x3 - 32x2 + 725x - 4984

Answer 1

ok HI!!
lets knock this out quick

Answer 2

Thank you!

Answer 3

gonna start with \[(x-4)(x+14)\] and then multiply it by a polynomial with zeros at \(5+8i\) and \(5-8i\)

Answer 4

there are a couple ways to find that quadratic
one is hard, one is easy and one is real real easy
you pick

Answer 5

Let's do the real real easy one haha

Answer 6

ok
the quadratic with zeros as \(a+bi\) is \[x^2-2ax+(a^2+b^2)\]
in your case \(a+bi=5+8i\) so the quadratic is \[x^2-2\times 5x+(5^2+8^2)=x^2-10x+89\]

Answer 7

final job is to multiply \[(x-4)(x+14)(x^2-10x+89)\] the algebra is a real pain so lets let the computer do it

Answer 8

Okay wait

Answer 9

http://www.wolframalpha.com/input/?i=%28x-4%29%28x%2B14%29%28x^2-10x%2B89%29

Answer 10

x^4−67x^2+1450x−4984?

Answer 11

looks good to me

Answer 12

easy enough right?q

Answer 13

cute dog btw

Answer 14

Yes thank you so much!

Answer 15

\[\color\magenta\heartsuit\]