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Question

The minimum possible value of the sum of squares of the roots of the equation x2+(a+3)x(a+5)=0 is


A

1

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B

2

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C

3

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D

4

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Solution

The correct option is C

3


Given equation is x2+(a+3)x(a+5)=0
Let ‘p’ and ‘q’ be the roots of the given equation.
Then, p + q = -(a+3) and pq = -(a+5)
So, p2+q2=(p+q)22pq
[(a+3)]22[(a+5)]
(a+3)2+2(a+5)
a2+9+6a+2a+10
a2+8a+19
(a+4)2+3
Minimum possible value is 3, as (a+4)2 is never negative.


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