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 . find the value of p and q

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Answer 1

Answer:

Correct option is

C

p=3,q=1 or p=−3,q=−1

x  

2

+(p+iq)x+3i=0

α+β=−(p−iq),αβ=3i

α  

2

+β  

2

=(α+β)  

2

−2αβ=[−(p+iq)]  

2

−6i

=(p  

2

−q  

2

)+i(2pq−6)=8

⇒p  

2

−q  

2

=8 and pq=3

⇒p=3,q=1 or p=−3,q=−1

Step-by-step explanation: