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Viktor [21]
3 years ago
15

Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero.

Mathematics
1 answer:
Nady [450]3 years ago
3 0

Answer:

x_4 = -5 + i

Step-by-step explanation:

See comment for complete question.

From the complete question, we have:

Zeros \to -2, -6, -5-i

Required

Determine the other zero

The zeros can be represented as:

x_1 = -2

x_2 = -6

x_3 = -5-i

Considering the 3rd zero, which is a complex number.

If a polynomial has a complex number as one of its zeros, then its conjugate pair is the corresponding zero

A conjugate pair is given as:

a + bi and a - bi

For x_3 = -5-i

The conjugate pair is:

x_4 = -5 + i

Hence, the other zero is: -5 + i

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