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Let a+b/a = A
x^2 +( A+1/A )x+1
roots are
-b+-√(b^2-4ac) /2a
(-A^2-1)/A +√{(A^2 +1)^2-4 /2a
-A^2 -1/A +√{( A^4 +2A^2 +1 -4A^2) /A^2 } /2A
{(-A^2 -1)/A + (A^2-1)/A }/2
-1/A
-(a+b/a)
other root
(-2A^2/A) /2
-A
-(a+b/a)
so roots are - (a+b/a) and -(a+b/a)
x^2 +( A+1/A )x+1
roots are
-b+-√(b^2-4ac) /2a
(-A^2-1)/A +√{(A^2 +1)^2-4 /2a
-A^2 -1/A +√{( A^4 +2A^2 +1 -4A^2) /A^2 } /2A
{(-A^2 -1)/A + (A^2-1)/A }/2
-1/A
-(a+b/a)
other root
(-2A^2/A) /2
-A
-(a+b/a)
so roots are - (a+b/a) and -(a+b/a)
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