Finding Complex Zeros. Find all zeros of the polynomial. P(x)=x^{3}+2x^{2}+4x+8

Danelle Albright

Danelle Albright

Answered question

2021-12-09

Finding Complex Zeros. Find all zeros of the polynomial.
P(x)=x3+2x2+4x+8

Answer & Explanation

yotaniwc

yotaniwc

Beginner2021-12-10Added 34 answers

Step 1
Given polynomial is:
P(x)=x3+2x2+4x+8
Factorizing we get,
P(x)=x2(x+2)+4(x+2)
P(x)=(x+2)(x2+4)
Step 2
Therefore the zeroes of f(x) are obtained on solving the equation:
P(x)=0
(x+2)(x2+4)=0
(x+2)=0;(x2+4)=0
x=-2; x=2i; x=-2i
Hence the real zero of P(x) is x = -2 and the complex zeroes of f(x) are x = 2i and x = -2i.

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