Let a 1 , a 2 ,… , a n be fixed real numbers and define a function f (x) = ( x − a 1 ) ( x − a 2 )...( x − a n ) . What is ? For some compute .

Question

Philoid · Accepted Answer

Given function is f(x) = (x – a₁) (x – a₂) … (x – a_n)

:

⇒

=

= (a₁ – a₁) (a₁ – a₂) … (a₁ – a_n) = 0

∴

:

⇒

=

= (a – a₁) (a – a₂) … (a – a_n)

∴

Ans. and

Let a1, a2,… , an be fixed real numbers and define a functionf (x) = ( x − a1) ( x − a2)...( x − an) .What is ? For some compute .