Question

determine all the zeros of x^3+5x^2-2x-10 if two of its zeros are √2 and -√2

Answer 1

Heya !!!




Given that,

-✓2 and ✓2 are two zeroes of the given polynomial





( X + ✓2) ( X - ✓2) are also factor of the given polynomial X³+5X²-2X-10.





( X + ✓2) ( X - ✓2) = X² -2





G(X) = X²-2




And


P(X) = X³ +5X² -2X -10




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





X² -2 ) X³ + 5X² - 2X - 10 ( X +5



***"***X³ *********-2X



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


***********+5X²******-10



***********+5X²*****-10



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




Remainder = 0





And,




Quotient = X + 5





( X + 5) = 0



X = -5



Hence,



✓2 , -5 and -✓2 are three zeroes of the cubic polynomial X³ + 5X² - 2X - 10.





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