Question

7) Resolve into factors:
x²-3x-(a²-a-2)​

Answer 1

Answer:

:

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