Given f(x) = 2x2 – x+ k, and the remainder when f(x) is divided by x – 1 is 3, then what is the value of k?

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.