(iii) p(x) = kx² – √2 x + 1
Putting x – 1 = 0, we get, x = 1
Using remainder theorem, when p(x) = kx² – √2 x + 1 is divided by x – 1, remainder is given by p(1)
= k(1)² – √2(1) + 1
= k – √2 + 1
Since x – 1 is a factor of p(x), hence remainder p(1) = 0
⇒ k – √2 + 1 = 0
⇒ k = √2 – 1