Find the value of a for which one root of the equation x2+(2a−1)x+a2+2=0 is twice as large as the other.

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x2+(2a−1)x+a2+2=0 

letonerootbeα

otherroot=2α 

sumofroots

3α=1−2a   

α=31−2a

 productofroots

2α2=a2+2  

 2(31−2a)2=a2+2   

2(4a2−4a+1)=9a2+18   

a2+8a+16=0   

(a+4)2=