Find all the zeros of (2x4 ‒ 3x3 ‒ 5x2 + 9x ‒ 3), it being given that two of its zeros are √3 and – √3.
Let us assume f (x) = 2x4 - 3x3 ‒ 5x2 + 9x - 3
As 
and – 
are the zeros of the given polynomial therefore each one of (x - 
) and (x + 
) is a factor of f (x)
Consequently, (x – 
) (x + 
) = (x2 – 3) is a factor of f (x)
Now, on dividing f (x) by (x2 – 3) we get:
f (x) = 0
2x2 - 3x2 – 5x2 + 9x - 3 = 0
(x2 – 3) (2x2 – 3x + 1) = 0
(x2 - 3) (2x2 – 2x – x + 1) (2x – 1) (x - 1) = 0
(x – 
) (x + 
) (2x – 1) (x - 1) = 0
∴ x = 
or x = - 
or x = 
or x = 1
Hence, all the zeros of the given polynomial are 
, -
, 
and 1
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