If -4, √5 and 13/2 are roots of the polynomial the other root is -√5.
How to determine roots of polynomial.
Given that the zeros are
-4, √5 and 13/2.
Meanwhile, the surds roots of a polynomial occurs in congugate pairs.
If +√a is a root of polynomial, then -√a is also a root.
Since √5 is a root of the polynomial, -√5 is a root of the polynomial too.
The polynomial is of degree four. This indicates that it has at most points where it touches or crossed the x- axis.
Therefore, if -4, √5 and 13/2 are roots the other root is -√5.