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2014-08-21T02:15:40+05:30

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If x + 2 is HCF of a  x^{2} - b x -c \ \   and \ \ b  x^{2}  - a x  + c \\ 


it means that x = -2 is  a root of the quadratic expressions and if you substitute x = -2 in the above expressions, their value is zero.

 4 a + 2b - c = 0 \\ 4b +2 a +c = 0 \\

Add the two equations. we get

 6 a + 6 b + 0 c = 0 \\ 6 a = - 6b \\ a = -b \\

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