Question

Which of the following is a polynomial with roots 5, 4i, and −4i? Walk me through please? Thanks.

Answer 1

x = 5 x = 4i x = -4i

Answer 2

(x - 5)( ? )( ? )

Answer 3

If a polynomial with real coefficients has complex roots, then the complex roots must come in complex conjugate pairs.

Answer 4

A polynomial with roots a, b, and c is the product of the factors (x - a)(x - b)(x - c)

x = 5 is a real root.
That means you have to have a factor x - 5.
Since 4i and -4i are complex conjugates, you have to have the factors x - 4i and x - (-4i). The last factor is x + 4i after simplification.

Answer 5

Now multiply the 3 factors together to find the polynomial.

Answer 6

so (x - 5)(x - 4i)(x + 4i), then multiply?

Answer 7

@mathstudent55

Answer 8

What you wrote above, the product of those three binomials, is already the correct polynomial.
Now you either have to or don't have to multiply them together depending on what your problem asks.
Your problem is worded "Which of the following polynomials ..." which seems to indicate that it has choices, but since I haven't seen the choices, I don't know what to compare the answer with.
If one choice is those three binomials multiplied together, that is correct.
If the choices show 3rd degree polynomials with an x^3 term, then multiply the three binomials together and compare the product with the choices.