Use the given information about a polynomial whose coefficients are real numbers to find the remaining zeros of the polynomial.
Degree: 6
Zeros: -6 + 13i^3,
-8 + s^2i,
-3 - 4i
i^3=-i
s^2i ???
To find the remaining zeros of the polynomial, we know that a polynomial with real coefficients has conjugate pairs of complex zeros. This means that for every complex zero, its conjugate is also a zero of the polynomial.
Let's consider the complex zeros:
1. Complex zero: -6 + 13i^3
Since i^3 = -i, we can rewrite the complex zero as -6 + 13(-i).
The conjugate of this complex zero is the same but with the opposite sign, so it is -6 - 13(-i) = -6 + 13i.
Therefore, the conjugate of -6 + 13i^3 is -6 + 13i.
2. Complex zero: -8 + s^2i
The conjugate of this complex zero is -8 - s^2i.
3. Complex zero: -3 - 4i
The conjugate of this complex zero is -3 + 4i.
Now we have found the conjugate pairs for all the complex zeros.
Therefore, the remaining zeros of the polynomial are:
-6 + 13i
-6 - 13i
-8 - s^2i
-3 + 4i