3.(i) Find the value of k, if x - 1 is a factor of p(x) in the following case:

   (i)    p(x) = x^2 + x + k

Answers (1)

Zero of polynomial   x - 1 is  1

If  x - 1  is factor of polynomial   p(x) = x^2 + x + k

Then,  p(1)  must be equal to zero 

Now,

\Rightarrow p(1) = (1)^2 + 1 + k

\Rightarrow p(1) =0

\Rightarrow 2+k = 0

\Rightarrow k = -2

Therefore,  value of k is -2

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