Please tell whether my answer is correct or not..?

Dear student , 

yes , the solution is correct .

But to multiply P(x) with 2 is conceptually not correct ( in 3rd line) 
When you start to find zeroes ,
write P(x) = 0 , THEN you can write
2x² - 2√2x - 3 = 0

Regards

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heavy questions
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I think it's correct . 
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No, it's wrong in second step you have done mistake. There multiplication must give 3 but it gives 6.
3? root 2 ?root 2= 3?2=6
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We can get it in this way

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What are you looking for?