if x - root 5 is a factor of the cubic polynomial xcube -3 root 5x square +13x -3 root 5 then find all the zeroes of thee polynomial

As x-root5 is a factor of the given cubic polynomial.

First do a long division till you get a remainder 0.

 

You will obtain a quadratic expression as quotient.

Find the roots of this expression.

 

Once you solve this, you will get the roots as

root 5,

root 5 + root 2 and

root 5 - root 2.