Question

please answer fast. 3 question all part . who will answer first he or she will mark as brainlist . ​

Answer 1

Answer:

1. k = -2
2. -(2+√2)
3. (√2-1)
4. 3/2

Step-by-step explanation:

The zero of x-1 is

$\huge \tt \underbrace \red{By \: \: Factor \: \: Theorem}$

i) (x-1) is a factor of p (x) , then p(1) = 0

$\huge \to \tt {1}^{2} + 1 + k = 0 \\ \huge \tt \to2 + k = 0 \\ \huge \tt \to k = - 2$

ii) (x-1) is a factor of p (x) , then p(1) = 0

$\huge \tt \to2 {(1)}^{2} + k(1) + \sqrt{2} = 0 \\ \huge \tt \to2 + k + \sqrt{2} = 0 \\ \huge \tt \to k = - (2 + \sqrt{2} )$

iii) (x-1) is a factor of p (x) , then p(1) = 0

$\huge \tt \to k {(1)}^{2} - \sqrt{2} + 1 = 0 \\ \huge \tt \to k = ( \sqrt{2} - 1)$

iv)(x-1) is a factor of p (x) , then p(1) = 0

$\huge \tt \to k {(1)}^{2} - 3 + k = 0 \\ \huge \tt \to2k - 3 = 0 \\ \huge \tt \to k = \frac{3}{2}$

Hope it helps ☺️