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Alejandro Christensen
Mathematics
5 May, 17:23
Find the polynomial from zeros
Zeros are 3i and 2-i
+1
Answers (
1
)
Jayden Simon
5 May, 17:45
0
Step-by-step 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.
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