Question

For the given function, find the zeros p(x)=-2x⁴(x+1)³(x-2)²

Answer 1

The zeros of the function p(x)=-2x⁴(x+1)³(x-2)² are x = 0 (multiplicity 4), x = -1 (multiplicity 3), and x = 2 (multiplicity 2).

Step-by-step explanation:

The zeros of the function p(x)=-2x⁴(x+1)³(x-2)² can be found by setting p(x) equal to zero and solving for x. We have:

-2x⁴(x+1)³(x-2)² = 0

Since a product is equal to zero if and only if one or more of its factors are equal to zero, we can set each factor equal to zero and solve for x:

x = 0 (multiplicity 4),

x+1 = 0 (multiplicity 3),

x-2 = 0 (multiplicity 2).

Therefore, the zeros of the function p(x)=-2x⁴(x+1)³(x-2)² are x = 0 (multiplicity 4), x = -1 (multiplicity 3), and x = 2 (multiplicity 2).