If a , b and c are numbers for which the equation x ( x − 3 ) 2 x 2 + 10 x − 36 = x a + x − 3 b + ( x − 3 ) 2 c is an identity, then a + b + c equals

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If a , b and c are numbers for which the equation x ( x − 3 ) 2 x 2 + 10 x − 36 ​ = x a ​ + x − 3 b ​ + ( x − 3 ) 2 c ​ is an identity, then a + b + c equals

TestHub · Accepted Answer

= hence x 2 + 10 x − 36 = a ( x − 3 ) 2 + b ( x − 3 ) x + c x put x = 0 ; − 36 = 9 a ⇒ a = − 4 x 2 + 10 x − 36 = x 2 ( − 4 + b ) + x ( 24 − 3 b + c ) + ( − 36 ) comparing coefficients also, − 4 + b = 1 ⇒ b = 5 24 − 15 + c = 10 ⇒ 9 + c = 10 ⇒ c = 1 a = − 4 ; b = 5 ; c = 1 i.e. a + b + c = 2

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