The function p(x) = x(x-5)(x-2)(x+3) has 4 zeros. what is the smallest zero?

The smallest zero (or root) is -3



Explanation:

Replace p(x) with 0. Then use the zero product property to solve

p(x) = x(x-5)(x-2)(x+3)
0 = x(x-5)(x-2)(x+3)
x(x-5)(x-2)(x+3) = 0
x = 0 or x-5 = 0 or x-2 = 0 or x+3 = 0
x = 0 or x = 5 or x = 2 or x = -3

The four roots are 
x = 0, x = 5, x = 2, and x = -3
these x values make p(x) equal to zero. The value x = -3 is the smallest of the list.