You might make use of the relationship between
 the coefficients and the sum and product of the
 roots of the quadratic equations. Without loss of
 generality you can take 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>&#x2267;</mo><mi>b</mi></mrow></math> and then
 you'll need to consider separately the case
 where 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>=</mo><mi>b</mi></mrow></math> and where 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>&#x003E;</mo><mi>b</mi></mrow></math>.

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