Questions: f(x)=(x+3)(x-1)^2(x-4)

Solution Steps

To find the roots of the polynomial function \( f(x) = (x+3)(x-1)^2(x-4) \), we need to set the function equal to zero and solve for \( x \). The roots are the values of \( x \) that make the function equal to zero. In this case, the roots can be found by setting each factor of the polynomial to zero.

We are given the polynomial function

\[ f(x) = (x + 3)(x - 1)^2(x - 4) \]

To find the roots, we set the function equal to zero:

\[ f(x) = 0 \]

The roots can be found by solving each factor of the polynomial:

1. \( x + 3 = 0 \) gives \( x = -3 \)
2. \( (x - 1)^2 = 0 \) gives \( x = 1 \) (with multiplicity 2)
3. \( x - 4 = 0 \) gives \( x = 4 \)

Thus, the roots of the function are:

\[ x = -3, \quad x = 1, \quad x = 4 \]

Final Answer