Question

It is known that a polynomial has solution if -1 and 3i. What is the lowest possible degree polynomial with these solutions? (1) 1 (2) 2 (3) 3 (4) 4

Answer 1

(3) the polynomial has degree 3. If it were a complex coefficient polynomial, then the answer is 2.

Explanation:

I am assuming it is a real coefficient polynomial, otherwise the answer will be 2. Since 3i is a root, then so is its conjugate -3i, therefore the polynomial is a multiple of (x-(-1)) *(x-3i) * (x-(-3i)) = (x+1) * (x²+9), which has real coefficients. Hence, its degree is atleast 3. Option (3) is correct