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Three roots of a polynomial equation with real coefficients are 3, 5 – 3i, and −3i. Which of the following numbers must also be a root of the equation?

a. 5 + 3i only
b. −3 and 5 + 3i only
c. 5 + 3i and 3i only
d. −3, 5 + 3i, and 3i

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sqdancefan

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Answer:

  c.  5 + 3i and 3i only

Step-by-step explanation:

The conjugates of the given complex roots must also be roots of the equation.

The conjugate of 5 -3i is 5 +3i.

The conjugate of -3i is 3i.

So, 5+3i and 3i must also be roots of the equation.

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