if (x+2) is a factor of xsquare+ax+2b and a+b=4 then a and b =
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Hi ,
Let p(x) = x² + ax + 2b
it is given that ,
( x + 2 ) is a factor of p( x ) , then
p( -2 ) = 0
=> ( -2 )² + a ( -2 ) + 2b = 0
=> 4 - 2a + 2b = 0
=> 2 - a + b = 0
=> - a + b = -2 ----( 1 )
a + b = 4 ----( 2 ) [ given ]
add equations ( 1 ) and ( 2 ) , we get
2b = 2
b = 2/2
b = 1
substitute b = 1 in equation ( 2 ), we get
a + 1 = 4
a = 4 -1
a = 3
Therefore ,
a = 3 , b = 1
I hope this helps you.
: )
Let p(x) = x² + ax + 2b
it is given that ,
( x + 2 ) is a factor of p( x ) , then
p( -2 ) = 0
=> ( -2 )² + a ( -2 ) + 2b = 0
=> 4 - 2a + 2b = 0
=> 2 - a + b = 0
=> - a + b = -2 ----( 1 )
a + b = 4 ----( 2 ) [ given ]
add equations ( 1 ) and ( 2 ) , we get
2b = 2
b = 2/2
b = 1
substitute b = 1 in equation ( 2 ), we get
a + 1 = 4
a = 4 -1
a = 3
Therefore ,
a = 3 , b = 1
I hope this helps you.
: )
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