Question

3 rd main. 3rd one I want the answer for it by step by step

Answer 1

$p(x) = k {x}^{2} - \sqrt{2} x + 1 \\ \\ p(1) = 0 \\ \\ k( {1)}^{2} - \sqrt{2} (1) + 1 = 0 \\ \\ k - \sqrt{2} + 1 = 0 \\ \\ k = \sqrt{2} - 1$

Answer 2

ʜᴇʏ ᴍᴀᴛᴇ!!

ʜᴇʀᴇ's ᴜʀ ᴀɴsᴡᴇʀ ᴅᴇᴀʀ:-)
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Apply remainder theorem 
=>x - 1 =0 
=> x =  1 

According to remainder theorem p(1) = 0 we get

Plug x = 1 we get  

P (1) = k(1)^2 – √2(1)+ 1

P(1) = K - √2  + 1

0 = K - √2  + 1 
√2  -1 = K 

Hence, the value of k is (√2-1).
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