Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and - √(5/3)

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and  - √(5/3)

Quotient is

x²+2x+1  

Compare the equation with  ax²  + bx  + c  = 0

We get

a = 1 ,b=2 c= 1

To factorize the value we have to find two value which

sum is equal to b     = 2

product is       a*c   =1*1 = 1

 1 and 1 are required values which

sum is      1 + 1   = 2

product is  1 * 1   = 1

So we can write middle term  2x  = x  + x 

We get

x² + x + x + 1 =0

x (x +1) +1(x +1) = 0

( x + 1)( x + 1)            = 0

x+1 = 0 , x+1 = 0

x= -1 , x= - 1

so our zeroes are   

 - 1  -1 , √(5/3) and  - √(5/3)