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2016-05-07T19:03:40+05:30

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We know that  \sqrt{2} and - \sqrt{2} are it's zeroes.
Hence,
(x+ \sqrt{2})(x- \sqrt{2})   is a factor.
We can get the other by dividing given polynomial by this one.
  =  \frac{ x^{4}-5 x^{3}+2 x^{2} +10x-8  }{(x+ \sqrt{2})(x- \sqrt{2})  }  \\  \\  \frac{x^{4}-5 x^{3}+2 x^{2} +10x-8  }{ x^{2} -2}
Solving this, we get:
 x^{2} -5x+4 \\  \\  x^{2} -x-4x+4 \\  \\ x(x-1)-4(x-1) \\  \\ (x-4)(x-1) \\  \\
x=4 or x=1

The other zeroes are: 4 and 1
0
If you don't get the division part tell me I'll modify the answer.
2016-05-08T02:15:15+05:30

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