We use synthetic division to divide by the given roots:
1 | 1 -11..40 -55..25
.....1....1 -10..30 -25
5 | 1 -10..30 -25 | 0
.....1....5 -25..25
.....1...-5....5 | 0
(The dots have been added as spacers for legibility.)
We're left with x^2-5x+5 which has irrational zeroes given by the quadratic formula:
(5-sqrt(5))/2=1.382 and (5+sqrt(5))/2=3.618. These are the missing zeroes.
A sketch of the graph shows f(0)=25, i.e., f(x)>0 when x<1; it dips below the x axis between x=1 and (5-sqrt(5))/2 and for (5-sqrt(5))/2<x<(5+sqrt(5))/2 f(x)>0; f(x)>0 when x>5. This makes 3 zones where f(x)>0.