Question

A polynomial function had -5+ root 3i as a root which of the following must also be a root of the function

Answer 1

Answer:

  none of the above (talk to your teacher about this)

Step-by-step explanation:

If a polynomial has real coefficients, complex roots come in conjugate pairs.

A root of $-5+\sqrt{3} i$ will have a conjugate of $-5-\sqrt{3}i$, which will also be a root.

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Here, it looks like the given root is $-5+\sqrt{3i}$, which is different from $-5+\sqrt{3}i$. None of the listed choices is the complex conjugate of this value.

The value of $-5+\sqrt{3i}$ is ...

  $-5+\sqrt{3i}=-5+(\sqrt{\dfrac{3}{2}}+\sqrt{\dfrac{3}{2}}i)$

so its conjugate is ...

  $(-5+\sqrt{3i})^*=-5+\sqrt{\dfrac{3}{2}}-\sqrt{\dfrac{3}{2}}i=\boxed{-5+\sqrt{-3i}}$

You will note that this is not among the answer choices.

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Additional comment

When a problem like this has an error in its presentation, we highly recommend you discuss it with your teacher (to get it corrected or deleted for future students). If you feel you must select one of the (erroneous) answer choices, your computer will probably accept the choice of $-5-\sqrt{3i}$, the first one.

Answer 2

Answer:it’s A

Step-by-step explanation:

I got it right on edg