Question

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

Answer 1

`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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