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

Answer 1

For the real roots, you get factors of the form x-a. In this case, (x-5) and (x+3) are factors. In the case of the complex root, it works similarly, but we also need the conjugate. That means (x+1-3i) and (x+1+3i) are both factors. Multiply the four factors together, combine like terms, and you will have your answer.

Answer 2

do we foil them together?

Answer 3

\[(x-5)(x+3)(x+1-3i)(x+1+3i)=(x^2-2x-15)(x^2+2x+10)\]

Answer 4

You should be able to finish from there.

Answer 5

thank you! I understand it now

Answer 6

No sweat. Do math every day.

Answer 7

I did not find the right answer

Answer 8

f(x) = x4 + 12.5x2 - 50x - 150

f(x) = x4 - 4x3 + 15x2 + 25x + 150

f(x) = x4 - 4x3 - 15x2 - 25x - 150

f(x) = x4 - 9x2 - 50x - 150

Answer 9

those are my options

Answer 10

@AnimalAin

Answer 11

\[(x^2−2x−15)(x^2+2x+10)\]\[=x^2(x^2−2x−15)+2x(x^2−2x−15)+10(x^2−2x−15)\]\[=x^4−2x^3−15x^2+2x^3−4x^2−30x+10x^2−20x−150\]\[=x^4-9x^2-50x-150\]

Answer 12

Looks like answer D. Make sure you pay attention to detail when you are working out your multiplication.

Answer 13

thank you!

Answer 14

do you know half angle rules for cos?

Answer 15

In particular...?

Answer 16

i figured it out

Answer 17

Excellent. Do math every day.