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How do you write a polynomial function with minimum degree whose zeroes are -1, 2, 3i?

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Mar 29, 2018

Answer:

#x^4-x^3+7x^2-9x-18#

Explanation:

If #3i# is zero of this polynomial, #-3i# is also zero of it. Hence

#P(x)=(x-(-1))(x-2)(x-3i)(x-(-3i))#

=#(x+1)(x-2)(x-3i)(x+3i)#

=#(x^2-x-2)(x^2+9)#

=#x^4-x^3+7x^2-9x-18#

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