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Bingel [31]
3 years ago
6

Which of the following is a polynomial with roots 5, 4i, and −4i?

Mathematics
2 answers:
Airida [17]3 years ago
7 0

If a <u>polynomial</u> has <u>roots </u>5, 4i and -4i, then it can has such three <u>factors</u>:

  1. x-5;
  2. x-4i;
  3. x-(-4i)=x+4i.

Therefore, the expression for this polynomial is

f(x)=(x-5)(x-4i)(x+4i).

Since

(x-4i)(x+4i)=x^2-(4i)^2=x^2-16i^2=x^2-16\cdot (-1)=x^2+16,

then

f(x)=(x-5)(x^2+16)=x^3-5x^2+16x-80.

Answer: correct choice is B

Leni [432]3 years ago
6 0
(x-4i)(x+4i)=x^2+16
(x^2+16)(x-5)=x^3-5x^2+16x-80
Answer is B
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