X²+3x-(1/a²+1/a-2)solve it as fast as you can
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x² + 3 x - ( 1/a² + 1/ a - 2 ) = 0
==> x² + 3 x - ( 1/a² + 2 /a- 1/ a - 2 ) = 0
==> x² + 3 x - ( 1/a ( 1/a + 2 ) - 1 ( 1/a + 2 ) ) = 0
==> x² + 3 x - ( 1/a + 2 )( 1/a - 1 ) = 0
==> x² + ( x/a + 2 x - x/a+ x ) - ( 1/a + 2 )( 1/a - 1 ) = 0
==> x² + x( 1/a + 2 ) - x ( 1/a - 1 ) - ( 1/a + 2 )( 1/a - 1 ) = 0
==> x ( x + 1/a + 2 ) - ( 1/a - 1 ) ( x + 1/a + 2 )
==> ( x + 1/a + 2 )( x - 1/a + 1 ) = 0
Either
x + 1/a + 2 = 0
==> x = - 1/a - 2
or
x - 1/a + 1 = 0
==> x = 1/a - 1
The roots are :
x = - 1/a - 2
x = 1/a - 1
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