Resolve into factors
x²-3x-(a²-a-2)
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Step-by-step explanation:
:
x² + 3 x - ( a² + a - 2 ) = 0
==> x² + 3 x - ( a² + 2 a - a - 2 ) = 0
==> x² + 3 x - ( a ( a + 2 ) - 1 ( a + 2 ) ) = 0
==> x² + 3 x - ( a + 2 )( a - 1 ) = 0
==> x² + ( ax + 2 x - ax + x ) - ( a + 2 )( a - 1 ) = 0
==> x² + x( a + 2 ) - x ( a - 1 ) - ( a + 2 )( a - 1 ) = 0
==> x ( x + a + 2 ) - ( a - 1 ) ( x + a + 2 )
==> ( x + a + 2 )( x - a + 1 ) = 0
Either
x + a + 2 = 0
==> x = - a - 2
or
x - a + 1 = 0
==> x = a - 1
The roots are :
x = - a - 2
x = a - 1
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