Astudent 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.

explain your answer. you!

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

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)