-Use the given zero to find all the zeroes of the function:
function: f(x)=2x^3+3x^2+50x+75
zero: 5i
Thank you!!
$\displaystyle 5i$ is a zero of f implies that its conjugate $\displaystyle -5i$ is also a zero of f then both $\displaystyle (x - 5i)$ and $\displaystyle (x + 5i)$ are factors of f and their product $\displaystyle x^2 + 25$ is a factor of $\displaystyle 2x^3 + 3x^2 + 50x + 75 $
The quotient $\displaystyle 2x^3 + 3x^2 + 50x + 75$ is divided by $\displaystyle x^2 + 25$is $\displaystyle 2x + 3$
$\displaystyle \therefore f(x)$ $\displaystyle = 2x^3 + 3x^2 + 50x + 75 = (x - 5i)(x + 5i)(2x + 3)$ zeros of f are 5i, -5i, and -3/2