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If ax2 + bx + c and bx2 + ax +-c have a common factor (x + 1) then show that a = b and c =’0.

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Given that (x + 1) is the factor of f(x) = ax2 + bx + c

from (1) and (2) 

a – b + c = b – a + c

⇒ a – b = b – a 

⇒ a + a = b + b 

⇒ 2a = 2b 

∴ a = b 

if a = b, from equation (1) 

c = 0

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