Write a third-degree polynomial in standard form with roots x

Tahmid Knox

Tahmid Knox

Answered question

2021-08-18

Write a third-degree polynomial in standard form with roots x = 4 and x - 2i. f(x)=a(x4)(x2i)(x+2i)

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-08-19Added 99 answers

By expanding,
f(x)=a(x4)(x22ix+2ix+4)
f(x)=a(x4)(x2+4)
f(x)=a[x2(x4)+4(x4)]
f(x)=a(x34x2+4x16)
For simplicity, use a=1. So, a possible third-degree polynomial is:
f(x)=1(x34x2+4x16)
f(x)=x34x2+4x16

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