Find the value of k, if x=1 is a factor of p(x) in each of the following cases: (i) p(x) = x² + x + k (ii) p(x) = 2x² + kx + √2 (iii) p(x) = kx² - √2x + 1 (iv) p(x) = kx² - x + k

If x=1 is the factor of the equation then put x=1 in these equations
(i) x² + x + k = 0 ⇒ (1)² + 1 + k = 0 ⇒ 1 + 1 + k = 0 ⇒ k = -2
(ii) 2x² + kx + √2 = 0 ⇒ 2(1)² + k(1) + √2 = 0 ⇒ 2 + k + √2 = 0 ⇒ k = -2 - √2
(iii) kx² - √2x + 1 = 0 ⇒ k(1)² - √2(1) + 1 = 0 ⇒ k - √2 + 1 = 0 ⇒ k = √2 - 1
(iv) kx² - x + k = 0 ⇒ k(1)² - (1) + k = 0 ⇒ k - 1 + k = 0 ⇒ 2k = 1 ⇒ k = 1/2