Answered

Which of the following is a polynomial with roots 3, 5i, and −5i?


f(x) = x3 − 3x2 + 25x − 75

f(x) = x3 − 3x2 + 15x − 25

f(x) = x3 − 15x2 + 25x − 75

f(x) = x3 − 3x2 + 15x − 75

Verified Answer :

Benjamin16

\(x_{1}=3 \\ \\ x_{2}=5i \\ \\ x_{2}=-5i \\ \\ f(x)=(x-x_{1})(x-x_{2})(x-x_{3})=(x-3)(x-5i)(x+5i)= \\ \\ =(x-3)(x^{2}+25)=x^{3}+25x-3x^{2}-75=x^{3}-3x^{2}+25x-75\)

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