Question

In the quadratic equation x² + (p + iq) x + 3i = 0, p & q are real. If the sum of the squares of the roots is 8 then 

(A) p = 3, q = – 1 

(B) p = 3, q = 1 

(C) p = –3, q = – 1 

(D) p = – 3, q = 1 

Answer 1

Correct option is (B,C)

Explanation:

x ²+(p+iq)^x + 3i = 0  

α² + β² = 8 

(α + β) = –(p + iq) 

αβ = 3i 

⇒(α + β)²  = 8 + 6i = p² – q ² + 2ipq 

p² – q² = 8 

2pq = 6 

⇒p = 3, q = +1 orp = –3, q = –1