3.) If 8 − 3𝑖 is a solution to a polynomial equation 𝑃(𝑥) = 0, which of the following must be

Question

another solution to the equation?
a. 3 − 8𝑖
b. 8 + 3𝑖
c. 3 − 3𝑖
d. 8 − 3𝑖

Answer 1

b. 8 + 3𝑖

Complex roots of polynomial equations occur in conjugate pairs. This means that if 8 − 3𝑖 is a solution to the polynomial equation 𝑃(𝑥) = 0, then its conjugate 8 + 3𝑖 must also be a solution. This is because complex roots always occur in pairs with their conjugates.