Find all the zeroes of the polynomial $negative 2 square root of 2 straight x cubed minus 18 straight x squared plus 24 square root of 2 straight x plus 72$ given that $2 square root of 3 space straight x to the power of 4 space and space minus 2 square root of 3$ are two of its zeroes.

Since two zeroes are $2 square root of 3 space and space minus 2 square root of 3$
$rightwards double arrow$ $left parenthesis straight x minus 2 square root of 3 right parenthesis space left parenthesis straight x plus 2 square root of 3 right parenthesis space equals space straight x squared minus 12$ is a factor of the given polynomial.
Now,
Since two zeroes are is a factor of the given polynomia
Now, $straight x to the power of 4 minus 2 square root of 2 straight x cubed minus 18 straight x squared plus 24 square root of 2 straight x plus 72$
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$equals left parenthesis straight x plus 2 square root of 3 right parenthesis space left parenthesis straight x minus 2 square root of 3 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets straight x left parenthesis straight x minus 3 square root of 2 right parenthesis space plus space square root of 2 left parenthesis straight x minus 3 square root of 2 right parenthesis close square brackets$

= $left parenthesis straight x plus 2 square root of 3 right parenthesis space left parenthesis straight x minus 2 square root of 3 right parenthesis space left parenthesis straight x plus square root of 2 right parenthesis space left parenthesis straight x minus 3 square root of 2 right parenthesis$
Hence, other zeroes are
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Find all the zeroes of the polynomial given that are two of its zeroes.

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Find all the zeroes of the polynomial $negative 2 square root of 2 straight x cubed minus 18 straight x squared plus 24 square root of 2 straight x plus 72$ given that $2 square root of 3 space straight x to the power of 4 space and space minus 2 square root of 3$ are two of its zeroes.