Question

find all the zeroes of the polynominal 3x4 6x4 2x2-10x-5 if two of its zeros are 5/3 and -5/3

Answer 1

Since it's two zeroes are 5/3 and -5/3.
Therefore, divisor=(x-5/3)(x+5/3)
=x^2-5/3
Then divide 3x4+6x3-2x2-10x-5 by x^2-5/3.
The answer will be 3x2+6x+3.
To find other zeroes factorize the answer:-
3x2+6x+3=0
3x2+3x+3x+3=0
3x(x+1)+3(x+1)=0
(3x+3)(x+1)=0
x=-3/3 or -1
The other zeroes are -1 and-1.
You didn't put signs in between but I have made it