Find the value of k, if x-1 is a factor of p(x) in each of the following cases :
(i) `p(x)=x^(2)+x+k " " (ii) p(x)=2x^(2)+kx+sqrt(2)`
(iii) `p(x)=kx^(2)-sqrt(2)x+1 " " (iv) p(x) =kx^(2)-3x+k`

Explanation

To find the value of \( k \) for each polynomial \( p(x) \) such that \( x - 1 \) is a factor, we will use the Factor Theorem. According to the theorem, if \( x - 1 \) is a factor of \( p(x) \), then \( p(1) = 0 \).

Let's solve each case step by step.

### (i) \( p(x) = x^2 + x + k \)

1. Substitute \( x = 1 \) into \( p(x) \):
\[
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