Question

find all the zeroes of polynomial 2x cube +x square -6x-3 if two of its zeroes are -roots and root3

Answer 1

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Answer 2

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Given that,


- root 3 and root 3 are the two zeroes of the given polynomial.





( X + root 3) ( X - root 3 ) are also factor of the given polynomial.




Now,




( X + root 3) ( X - root 3) = X² -3






G(X) = X² -3



And,




P(X) = 2X³ + X² -6X - 3



On dividing P(X) by G(X) we get,





X² -3 ) 2X³ + X² - 6X - 3 ( 2X +1



*********2X³******-6X




-------------------------------------------


******0*****+X²****0*****-3




************+X²**********-3




-------------------------------------------

Remainder = 0




We get,




Reminder = 0




And,


Quotient = 2X + 1





2X + 1 = 0



2X = -1



X = -1/2




Hence,



-1/2 , root 3 and - root 3 are three zeroes of the polynomial 2X³+X²-6X - 3.





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