I don't understand exactly what it wants. So is it asking for a function like this:
They have 1 zero, They have no zeroes:
And when you add these two function they have 2 zeros.
Am I correct?
Perhaps this will help:
Assuming we are talking about real zeroes....
Let one function be 2( x - 2) ^2 = 2 x^2 - 8 x + 8 whch has one zero at x = 2
Let the second be -x^2 - 17 which has no real zeroes
So....their sum is
x^2 - 8x - 9 factor
(x - 9) (x + 1)
The zeroes are x = 9 and x = -1
See the graphs here : https://www.desmos.com/calculator/fre2biof7f