document.write( "Question 1014628: Is it possible for a polynomial function to have no rational zeroes but to have real zeros? If so, give an example. So, I was also confused on the difference between real and rational zeros, does the rational root test have a play? \n" ); document.write( "

Algebra.Com's Answer #630939 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( "Yes
\n" ); document.write( ".
\n" ); document.write( "x^2-3=0
\n" ); document.write( ".
\n" ); document.write( "roots (zeroes) at +/- $\"sqrt%283%29\"$
\n" ); document.write( "The roots are real, but not rational.
\n" ); document.write( "(The square root of three is not rational)
\n" ); document.write( "Real (not complex) roots are always x-intercepts
\n" ); document.write( "on the graph of the function. Imaginary roots are not.
\n" ); document.write( ".
\n" ); document.write( "On the graph below:
\n" ); document.write( ".
\n" ); document.write( " $\"f%28x%29=x%5E2-3\"$ Red line below, has irrational real roots
\n" ); document.write( ".
\n" ); document.write( " $\"f%28x%29=x%5E2%2B3\"$ Green line below, has imaginary (not real) roots,
\n" ); document.write( "and does not intercept x axis.
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+800%2C+800%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-3%2C+x%5E2%2B3%29+\"$
\n" ); document.write( ".
\n" ); document.write( "The rational roots test gives possible rational roots.
\n" ); document.write( "If there are rational roots,they are given by this test.
\n" ); document.write( "The test does not determine if any of the possibilities
\n" ); document.write( "are actually roots. \n" ); document.write( "

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