Question

Find all real and complex zeros of the following polynomial f(x)=x^(3)-3x^(2)+25x-75

Answer 1

Hi,

Explanation:

`x^3-3x^2+25x-75=x^2(x-3)+25(x-3)\\\\=(x-3)(x^2+25)\\\\=(x-3)(x^2-25i^2)\\\\f(x)=(x-3)(x-5i)(x+5i)\\\\Zeros\ are\ \{3,5i,-5i \}`