Question

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!

Answer 1

See explanation

Explanation:

1. The student is wrong because imaginary roots always occur in conjugate pairs.

So -4i cannot be the only imaginary root. It has to be accompanied by 4i also.

2. So the 2 roots can be 4i and -4i.

therefore the equation can be

(x - 4i)(x + 4i) = 0

`x^(2)` + 16 = 0