Respuesta :

VirαtKσhli

Given :-

  • f(x) = 2x² - x + k .
  • When f(x) is divided by (x-1) , the remainder is 3 .

To Find :-

  • The value of k .

Solution :-

Here we are given that ,

→ f(x) = 2x² - x + k

  • By Remainder Theorem , if f(x) is divided by x-a , then the remainder is f(a) .
  • Hence here is f(x) is divided by x-1 , then the remainder will be f(1) . On substituting x = 1 , we have ,

→ f(x) = 2x² - x + k

→ f(1) = 2(1)² - 1 + k

  • f(1) = 3 ,

→ 3 = 2*1 -1 + k

→ 2 -1 + k = 3

→ k +1 = 3

→ k = 3-1

→ k = 2

Hence the value of k is 2 .

I hope this helps.

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