Question

Multiple Correct Answers Type
Q. In the quadratic equation x^2 + (p + iq) x + 3i = 0, p and q are real. If the sum of the squares of the roots is 8, then the ordered pair (p, q) is given by:
(A) (3, 1)
(B) (-3,-1)
(C) (-3,1)
(D) (3,-1)​

Answer 1

Answer:

OPTION A IS......

Step-by-step explanation:

....................................

Answer 2

Answer:

Thus ( p,q ) are

(3,1) or (-3,-1) so A and B are correct

Step-by-step explanation:

x² + (p + iq) x + 3i = 0

let the roots are a and b

then a+b=-(p+iq)

and ab=3i

Given a²+b²=8

(a+b)²-2ab=8

{-(p+iq) }²-2(3i) = 8

p²+i²q²+2ipq-6i=8

p²-q²+2pqi=8+6i

on ocmparison

p²-q²=8

and 2pq=6,pq=3

p²-q²=8

p²-(pq/p)²=8

p²-9/p²=8

let p²=m

m-9/m=8

m²-9=8m

m²-8m-9=0

(m-9)(m+1)=0

m=9 or -1

Or p²=9 or-1

p is real number

so p²=9 so p=3,-3

and q=pq/p

=3/3 or 3/-3

=1,-1

Thus ( p,q ) are

(3,1) or (-3,-1) so A and B are correct