Question

a student claims -4i is the only root of a quadratic polynomial equation that has real coefficients whats the students mistake and write one possible polynomial that has the correct roots from part a in standard form

Answer 1

If a quadratic equation has an imaginary root -4i, then its conjugate i.e. 4i will be the other root of the equation.

Step-by-step explanation:

a. The only imaginary root of a quadratic equation is -4i, this is not possible.

Because, if a quadratic equation has an imaginary root -4i, then it's conjugate i.e. 4i will be the other root of the equation.

b. So, the two roots of a quadratic equation are imaginary and they are 4i and -4i.

Therefore, the equation will be

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

⇒

⇒

⇒ (Answer)

Explanation: