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5 votes
Find a polynomial function with real coefficients that has the given zeros:

2, 5 + i

User Maxrodrigo
by
8.0k points

1 Answer

4 votes

By the complex conjugate root theorem, there must also be another zero -
5-i.

Therefore


f(x)=(x-2)(x-(5+i))(x-(5-i))\\f(x)=(x-2)(x-5-i)(x-5+i)\\f(x)=(x-2)((x-5)^2+1)\\f(x)=(x-2)(x^2-10x+25+1)\\f(x)=(x-2)(x^2-10x+26)\\f(x)=x^3-10x^2+26x-2x^2+20x-52\\f(x)=x^3-12x^2+46x-52

User Paschalis
by
8.8k points

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