Question

5. Determine the maximum number of real zeros.f
(x)=(x-1/3)^2(x-1)^3

Answer 1

The maximum number of real zeros of the function is 5.

Explanation:

Zeros of a polynomial

Any polynomial of positive order can have a maximum number of zeros equal to its order. For example, a quadratic function can have as many as two zeros.

The given polynomial is:

`f(x)=(x-1/3)^2(x-1)^3`

The order of this polynomial is 5 since it's factored as a quadratic polynomial by a cubic polynomial. The order is 2+3=5.

Thus, the maximum number of real zeros of the function is 5.