Step by step solution to "Find all the zeros, real and nonreal, of..."

Aneeka Hunt

Answered question

2021-08-17

Find all the zeros, real and nonreal, of the polynomial and use that information to express p(x) as a product of linear factors.

p (x) = x^{3} + 11 x

tafzijdeq

Skilled2021-08-18Added 92 answers

Step 1

p (x) = x^{3} + 11 x

Step 2
Find zeroes,

p (x) = 0

\Rightarrow x^{3} + 11 x = 0

\Rightarrow x (x^{2} + 11) = 0

\Rightarrow x = 0, x^{2} + 11 = 0

\Rightarrow x = 0, x = \pm \sqrt{11} i

linear factors are x,

(x - \sqrt{11} i) (x + \sqrt{11} i)

\Rightarrow p (x) = x (x - \sqrt{11} i) (x + \sqrt{11} i)

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