document.write( "Question 154464: is it true that all real polynomials of odd degree has at least one real root? if it's true, what's the proof? if it's false, can you give a counter example? \n" ); document.write( "

Algebra.Com's Answer #113733 by stanbon(75887) $\"\"$ $\"About$

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That would be true.
\n" ); document.write( "Take for example y = x^3
\n" ); document.write( "When x is very negative y is verty negative.
\n" ); document.write( "But when x is very positive y is very positive.
\n" ); document.write( "If the function is continuous the y values must
\n" ); document.write( "have passed through zero; that means the yvalues
\n" ); document.write( "must have intersected the x-axis where y is zero.
\n" ); document.write( "And that intersection would be a Real Number zero
\n" ); document.write( "for the function.
\n" ); document.write( "I said this about a cubic equation; the same would
\n" ); document.write( "be true of any odd-powered function.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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