document.write( "Question 427393: find all the REAL zeros of the function x^4-4x^3+4x-1 \n" ); document.write( "

Algebra.Com's Answer #297215 by Gogonati(855) $\"\"$ $\"About$

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Solution:First we factor the function:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E4-1%29-4x%28x%5E2-1%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-1%29%2A%28x%5E2%2B1%29-4x%28x%5E2-1%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-1%29%2A%28x%5E2%2B1-4x%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%29%28x%2B1%29%28x%5E2-4x%2B1%29\"$ To find all the zeros equalize to zero all the factors:\r
\n" ); document.write( "\n" ); document.write( "x-1=0 => x=1; x+1=0 => x=-1;\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-4x%2B1=0\"$ =>\r
\n" ); document.write( "\n" ); document.write( " $\"x=2%2B-+sqrt%283%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The solution set of this function is:{-1, 1, 2+-sqrt(3)}\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28400%2C+400%2C+-5%2C+5%2C+-16%2C+5%2C+x%5E4-4x%5E3%2B4x-1%29\"$ \n" ); document.write( "

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