p(x) bir polinomdur. P(x+1)+p(x-1)= 2x²+2x-2 olduguna gore p(x) polinomunun katsayılar toplamı kactır??



Sagot :

a(x+1)+b + a(x-1)+b = 2x²+2x-2 ise ax+a+b+ax-a+b = 2x²+2x-2  olur 2ax+2b = 2x²+2x-2 den a=1 b=-1 bulunur P(x)= ax+b de yerine yazarsak p(x)=x-1 katsayılar top. denince x yerine 1 yazılır bu durumda p(1)=1-1 den p(1)=0 olur.

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