Madhya Pradesh Police Exam Model Paper 6

Concept Used :
If (x - a) is a factor of f(x) then f(a) = 0
Solution:
∵ (x - 1) is a factor of ${\mathit{x}}^4-5{\mathit{x}}^3+\mathit{k}{\mathit{x}}^2-4\mathit{x}+5$
$\therefore \mathit{x}-1=0$
$\therefore \mathit{x}=1$ satisfy the given polynomial. So put x = 1 in given polynomial -
${\left(1\right)}^4-5{\left(1\right)}^3+\mathit{k}{\left(1\right)}^2-4\left(1\right)+5=0$
$\therefore 1-5+\mathit{k}-4+5=0$
$\therefore \mathit{k}=3$