1. ## polynomials

-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!!

2. Originally Posted by ss103
-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!!
$5i$ is a zero of f implies that its conjugate $-5i$ is also a zero of f then both $(x - 5i)$ and $(x + 5i)$ are factors of f and their product $x^2 + 25$ is a factor of $2x^3 + 3x^2 + 50x + 75$
The quotient $2x^3 + 3x^2 + 50x + 75$ is divided by $x^2 + 25$is $2x + 3$

$\therefore f(x)$ $= 2x^3 + 3x^2 + 50x + 75 = (x - 5i)(x + 5i)(2x + 3)$ zeros of f are 5i, -5i, and -3/2