Problem Set 7: Prove the following statement (using either direct or indirect proof method): For every real number ( x ), if ( x^{5}-4 x^{4}+3 x^{3}-x^{2}+3 x-4 geq 0 ), then ( x geq 0 ).

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Problem Set 7: Prove the following statement (using either direct or indirect proof method): For every real number  ( x  ), if  ( x^{5}-4 x^{4}+3 x^{3}-x^{2}+3 x-4  geq 0  ), then  ( x  geq 0  ).

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