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The fourth degree polynomial equation having one of the roots \( 1 + \sqrt{2} + 2\sqrt{3}\)

is \( x^{4} + bx^{3} + cx^{2} + dx + e = 0\)

Find 1 + b + c + d + e ( all are integers)

Details - Question appeared in Ramanujan Ganit Spardha 2014 Std XI and XII (Only Gujarat region)

for other problem click here

This exam motive is to just know how differently you can approach a basic question(and if we have a different and short method we are rewarded extra marks). So please write your method if you got your answer right.

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