Question

3. If a polynomial equation p(x) = 0 has 3 + 4i as a solution, what other solutions must it have?

A.3-I
B.4-3i
C.4+3i
D.3-4i

Answer 1

it must have di 3-4 I as another solution

Answer 2

Option (d) is correct.

For the given polynomial p(x) if 3 +4i is a root then, 3 - 4i is also the root of p(x).

Explanation:

Consider the given polynomial equation p(x) = 0

It is given that the polynomial P(x) has one root 3 + 4i

According to Complex conjugate theorem , if V is a polynomial and x + iy is a root of given polynomial then its conjugate x - iy is also the root of the polynomial.

Thus, for the given polynomial p(x) if 3 +4i is a root then, 3 - 4i is also the root of p(x).

Thus, option (d) is correct.