Obtain all zeros of the polynomial …

The given polynomial is:
f(x) = 2x³ - x² - 4x + 2.
It is given that the two zeroes of the above polynomial are {tex}\sqrt{2}{/tex} and -{tex}\sqrt{2}{/tex}   
Therefore, (x - {tex}\sqrt{2}{/tex})(x + {tex}\sqrt{2}{/tex}) = (x² - 2) is a factor of f(x).
Now we divide (x) = 2x³ - x² - 4x + 2 by (x²- 2), we obtain

Where quotient = (2x - 1)
{tex}\therefore{/tex}   f(x) = 0 {tex}\Rightarrow{/tex} (x² - 2)(2x - 1) = 0
{tex}\Rightarrow{/tex} (x - {tex}\sqrt{2}{/tex}) (x + {tex}\sqrt{2}{/tex})(2x - 1) = 0
{tex}\Rightarrow{/tex} (x - {tex}\sqrt{2}{/tex}) = 0 or (x + {tex}\sqrt{2}{/tex}) = 0 or (2 x -1) = 0
{tex}\Rightarrow{/tex} x = {tex}\sqrt{2}{/tex} or x = - {tex}\sqrt{2}{/tex} or x = {tex}\frac{1}{2}{/tex}.
Hence, all zeros of f(x) are {tex}\sqrt{2}{/tex}, -{tex}\sqrt{2}{/tex} and {tex}\frac{1}{2}{/tex}.