document.write( "Question 1040832: Find a cubic polynomial w/ integer coefficients & roots: positive 1, -1/4, and positive 3/2. \n" ); document.write( "

Algebra.Com's Answer #655762 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "Find a cubic polynomial w/ integer coefficients & roots: positive 1, -1/4, and positive 3/2.
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document.write( "What John said is an algorithm, i.e. a \"software\".\r\n" );
document.write( "To transform it into a \"hardware\", consider first the polynomial\r\n" );
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document.write( "p(x) =  = .\r\n" );
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document.write( "It has the assigned roots, obviously.\r\n" );
document.write( "When you open the parentheses, you will get the polynomial with rational coefficients, not with integer yet.\r\n" );
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document.write( "In order to get the polynomial with integer coefficients, mulptiply p(x) by the denominators of fractions 4*2. You will get\r\n" );
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document.write( "f(x) = 4*2*p(x) = .\r\n" );
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document.write( "This polynomial is exactly what you need. \r\n" );
document.write( "It has the given values as the roots and integer coefficients.\r\n" );
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document.write( "Notice that what I said is consistent with the solutions of the two other tutors.\r\n" );
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