Question

find all the zeroes of the polynomial f(x)=2x^4-3x^3-5x^2+9x-3, if two of its zeroes are +_root3

Answer 1

Heya !!!




Given that,



-✓3 and + ✓3 are two zeroes of the given polynomial.





(X - ✓3) ( X + ✓3) = X² - 3 is also factor of the given polynomial.





G(X) = X² - 3





P(X) = 2X⁴ - 3X³ - 5X² + 9X - 3




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



X² - 3 ) 2X⁴-3X³-5X²+9X-3 ( 2X² -3X +1



********2X⁴*****-6X²



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


************-3X³ + X² + 9X - 3




************-3X³*******+9X




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



**************+X² *********-3




*************X²***********-3



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





Remainder = 0






We get,




Remainder = 0



And,




Quotient = 2X²-3X+1






Factories the quotient then we will get two other zeroes of the given polynomial.





=> 2X² - 3X + 1






=> 2X² - 2X - X + 1




=> 2X ( X - 1 ) - 1 ( X - 1)






=> ( X -1) ( 2X -1) = 0





=> X = 1 OR X = 1/2






Hence,




-✓3 , 1 , 1/2 and ✓3 are four zeroes of the given polynomial 2X⁴-3X³-5X²+9X-3.






★ HOPE IT WILL HELP YOU ★

Answer 2

Answer:

Hope this helps you ✌️✌️