If n-k is a factor of the polynomials x^2+px +q and x^2+mx+n, prove that k = n+ n-k/m-p
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Hi ,
I think there is an error in the question.
plz , check.
Let f( x ) = x² + px + q ,
g( x ) = x² + mx + n ,
If ( x - k ) is a factor of f( x ) and g( x ) , then
f( k ) = g( k )
k² + pk + q = k² + mk + n
pk + q = mk + n
q - n = mk - pk
q - n = k ( m - p )
( q - n ) / ( m - p ) = k
Therefore ,
k = ( q - n )/(m - p )
I hope this helps you.
: )
I think there is an error in the question.
plz , check.
Let f( x ) = x² + px + q ,
g( x ) = x² + mx + n ,
If ( x - k ) is a factor of f( x ) and g( x ) , then
f( k ) = g( k )
k² + pk + q = k² + mk + n
pk + q = mk + n
q - n = mk - pk
q - n = k ( m - p )
( q - n ) / ( m - p ) = k
Therefore ,
k = ( q - n )/(m - p )
I hope this helps you.
: )
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