Find all zeros of f(x)=x^4-3x^3+6x^2+2x-60 given that 1+3i is a zero of f(x)

The roots of f(x) are: -2, 3, (1+3i) and (1-3i)

Step-by-step explanation:

We are given an expression:

(1+3i) is a root of f(x)

We have to find the remaining roots of f(x).

Since, (1+3i) is a root of f(x),

is a factor of given expression.

Now, we check if (1 - 3i) is a root of given function.

Thus, (1-3i) is also a root of given function.

Since, (1-3i) is a root of f(x),

is a factor of given expression.

Thus, we can write:

Dividing f(x) by above expression:

To find the root, we equate it to zero:

Thus, the roots of f(x) are: -2, 3, (1+3i) and (1-3i)

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step-by-step explanation: