If x + k is the HCF of x² + ax +b and x² + cx + d then what is the value of k ?
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x+k is HCF of x²+ax+b and x²+cx+d. Therefore x+k is a factor of each expression
Put x=-k in the given expressions.
(-k)²+a×(-k)+b=0
k²-a.k+b=0………………….(1)
(-k)²+c.(-k)+d=0
k²-c.k+d=0……………………(2)
Subtract eq.(2) from (1)
c.k-a.k-d+b=0
k(c-a)=d-b
k=(d-b)/(c-a)
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