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1 vote
Find the polynomial from zeros
Zeros are 3i and 2-i

User Pablobu
by
6.3k points

1 Answer

4 votes

Answer:


Explanation:

complex numbers always come in pairs. So you have 4 roots to this polynomial

y = (x - 3i)(x + 3i)(x - 2 + i)(x - 2 - i)

y = (x^2 - 9i^2)( (x - 2)^2 + i)( (x - 2)^2 - i)

y = (x^2 + 9) [( x - 2)^2 - i^2]

y = (x^2 + 9) [x^2 - 4x + 4 + 1]

y = (x^2 + 9) (x^2 - 4x + 5)

y = (x^4 - 4x^3 + 14x^2 - 36x + 45)

The graph is below. Notice it never crosses the x axis which you could have predicted from all the complex roots.

Find the polynomial from zeros Zeros are 3i and 2-i-example-1
User Victorbalssa
by
7.0k points
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