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A student claims that -4i is the only imaginary root of a quadratic polynomial equation that has real coefficients.

1. What is the student’s mistake?
2. Write one possible polynomial that has the correct roots from part a in standard form.

Please explain your answer. Thank you!

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MathPhys

Step-by-step explanation:

Complex roots or imaginary roots must come in conjugate pairs.  If -4i is a root, that means 4i is also a root.

A possible polynomial is:

y = (x + 4i) (x − 4i)

y = x² − 16i²

y = x² + 16

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