Question

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

3, -13, and 5 + 4i

Answer 1

@dumbcow

Answer 2

3 roots but one is a complex root. complex roots come in conjugate pairs if the coefficients of the polynomial are real.

so that means you need a 4th degree polynomial with real coefficients to satisfy the requirements.

Answer 3

Do you want to see the answer choices or does it matter?

Answer 4

so your roots need to be 3, -13, 5 + 4i and 5 - 4i. that menas your factors should be...

(x-3)(x+13)(x- 5 - 4i)(x - 5+4i)

Answer 5

multiply those out to get your answer.

Answer 6

f(x) = x^4 - 98x^2 + 800x - 1599

Answer 7

for imaginary roots, i like to use this method:

x = 5 + 4i

x-5 = 4i

(x-5)^2 = (4i)^2

x^2 -10x +25 = -16

x^2 -10x +41 = 0

polynomial:
---> (x-3)(x+13)(x^2 -10x+41)

Answer 8

Could you help me on 2 more @dumbcow ?

Answer 9

ok