Three zeroes of a fifth degree polynomial function are ⅓,4-6i, and -2+11i. Determine the remaining zeroes of the function.
the complex roots come in conjugate pairs...
4+6i, -2-11i
To determine the remaining zeroes of the function, we need to find the complex conjugates of the given complex zeroes. The complex conjugate of a complex number a + bi is a - bi, where a and b are real numbers.
The given complex zeroes are 4 - 6i and -2 + 11i. The complex conjugates of these zeroes are 4 + 6i and -2 - 11i, respectively.
Now we can write the polynomial function using the zeroes:
(x - 1/3)(x - 4 + 6i)(x - 4 - 6i)(x - (-2 + 11i))(x - (-2 - 11i))
To find the remaining zeroes, we can expand this function using algebraic methods or use a graphing calculator. Let's use a graphing calculator:
1) Enter the equation: (x - 1/3)(x - 4 + 6i)(x - 4 - 6i)(x - (-2 + 11i))(x - (-2 - 11i)) = 0.
2) Solve this equation to find the roots.
3) The roots obtained are the remaining zeroes of the function.
By following these steps, you should be able to determine the remaining zeroes of the function.