If 2+√5 i is a root of x2-p x+q=0 where p and q are real, then the ordered pair (p, q) is equal to

Question

If 2+√5 i is a root of x2-p x+q=0 where p and q are real, then the ordered pair (p, q) is equal to (A) (4,9) (B) (9,4) (C) (3,3) (D) (2,3)

Tardigrade Admin · Accepted Answer

As p, q ∈ R, other root of the equation is 2-i √5. Thus, p=4, q=(2+√5 i)(2-√5 i)=9

Q. If $2 + 5 i$ is a root of $x^{2} - p x + q = 0$ where $p$ and $q$ are real, then the ordered pair $(p, q)$ is equal to