Let f ( x ) = ( x − a 1 ) ( x − a 2 ) ( x − a 3 ) and g ( x ) = f ′ ( x ) . If α , β , γ are the roots of f ( x ) = 0 , then α β + β γ + γ α equals

Question

Let f ( x ) = ( x − a 1 ​ ) ( x − a 2 ​ ) ( x − a 3 ​ ) and g ( x ) = f ′ ( x ) . If α , β , γ are the roots of f ( x ) = 0 , then α β + β γ + γ α equals

TestHub · Accepted Answer

∑ α β = a 1 ​ a 2 ​ + a 2 ​ a 3 ​ + a 3 ​ a 1 ​ , while substituting x = 0 in g gives the same value.

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