document.write( "Question 885534: What are the zeroes of f(x) = x^3 + 5x^2 - 7x + 1? \n" ); document.write( "

Algebra.Com's Answer #535222 by Theo(13342) $\"\"$ $\"About$

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f(x) = x^3 + 5x^2 - 7x + 1
\n" ); document.write( "p = factors of the constant term.
\n" ); document.write( "q = factors of the leading term.
\n" ); document.write( "possible rational solutions are factors of p divided by factors of q.
\n" ); document.write( "this would make them +/- 1.
\n" ); document.write( "use synthetic division to see if either one of these is a rational root.
\n" ); document.write( "1 is a root which means that (x-1) is a factor.
\n" ); document.write( "the remainder of the synthetic division is x^2 + 6x - 1
\n" ); document.write( "the roots of this equation are x = -3 + sqrt(10) and -3 - sqrt(10)
\n" ); document.write( "this equation has 1 real rational root and 2 real irrational roots.
\n" ); document.write( "the real rational root is x = 1
\n" ); document.write( "the real irrational roots are -3 +/- sqrt(10)
\n" ); document.write( "a graph of your equation is shown below:
\n" ); document.write( "the dashed vertical lines show you where the roots are.
\n" ); document.write( "they are at x = 1, x = -3 - sqrt(10) and x = -3 + sqrt(10)
\n" ); document.write( "-3 - sqrt(10) is roughly equal to x = -6.16.
\n" ); document.write( "-3 + sqrt(10) is roughly equal to x = 0.16.
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